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<h3 class="wp-block-heading">Key Concepts</h3>



<ul class="wp-block-list">
<li>To understand angles and unit angles</li>



<li>To measure with unit angles</li>



<li>To measure and draw angles</li>



<li>To add and subtract angle measures</li>
</ul>



<h2 class="wp-block-heading"><strong>Understand Angles and Unit Angles</strong>&nbsp;</h2>



<h3 class="wp-block-heading"><strong>Angle:</strong>&nbsp;</h3>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5687.png" alt="Angle: " class="wp-image-24031" style="width:286px;height:218px" width="286" height="218" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5687.png 393w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5687-300x229.png 300w" sizes="auto, (max-width: 286px) 100vw, 286px" /></figure></div>


<p>An angle is the rotation of a ray from an initial point to a terminal point.&nbsp;</p>



<h2 class="wp-block-heading"><strong>Types of Angles:&nbsp;</strong>&nbsp;</h2>



<p>There are majorly six types of <a href="https://www.turito.com/learn/math/angle-and-arc-measures-grade-9" data-type="link" data-id="https://www.turito.com/learn/math/angle-and-arc-measures-grade-9">angles</a> in geometry: </p>



<ul class="wp-block-list">
<li><strong>Acute angle:</strong> It lies between 0° to 90°.&nbsp;</li>



<li><strong>Obtuse angle:</strong> It lies between 90° to 180°.&nbsp;</li>



<li><strong>Right angle:</strong> The angle which is exactly equal to 90°.&nbsp;</li>



<li><strong>Straight angle:</strong> The angle which is exactly equal to 180°.&nbsp;</li>



<li><strong>Reflex angle:</strong> The angle which is greater than 180° and less than 360°.&nbsp;</li>



<li><strong>Full rotation:</strong> The complete rotation of an angle equal to 360°.&nbsp;</li>
</ul>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5675-1024x252.png" alt="Types of Angles:  " class="wp-image-24016" style="width:744px;height:182px" width="744" height="182" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5675-1024x252.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5675-300x74.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5675-768x189.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5675.png 1474w" sizes="auto, (max-width: 744px) 100vw, 744px" /></figure></div>


<p><strong>Unit Angle:</strong>&nbsp;</p>



<ul class="wp-block-list">
<li>An angle is measured with units called degrees (ᵒ).&nbsp;</li>



<li>An angle that turns through 1 / 360&nbsp;of a circle is called a unit angle.&nbsp;</li>
</ul>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="568" height="165" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5688.png" alt="Unit Angle: " class="wp-image-24032" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5688.png 568w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5688-300x87.png 300w" sizes="auto, (max-width: 568px) 100vw, 568px" /></figure></div>


<p>Examples of angles with their measurements:&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5676-1024x431.png" alt="Examples of angles with their measurements: " class="wp-image-24017" style="width:711px;height:299px" width="711" height="299" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5676-1024x431.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5676-300x126.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5676-768x323.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5676.png 1517w" sizes="auto, (max-width: 711px) 100vw, 711px" /></figure></div>


<h3 class="wp-block-heading"><strong>Measure with Unit Angles</strong>&nbsp;</h3>



<p>Unit <a href="https://www.turito.com/learn/math/problems-using-angle-relationships-grade-7">angles</a> are measured using a smaller angle to <a href="https://www.turito.com/learn/math/measure-and-classify-angles-grade-9">measure</a> a larger angle by repeating the unit.&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5677.png" alt="Measure with Unit Angles " class="wp-image-24018" style="width:373px;height:382px" width="373" height="382" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5677.png 602w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5677-293x300.png 293w" sizes="auto, (max-width: 373px) 100vw, 373px" /></figure></div>


<p class="has-text-align-center"><em>Unit angle</em>&nbsp;</p>



<p><strong>Example:</strong>&nbsp;</p>



<p>What is the measurement of the smaller angle formed by the clock hands when it is 5 o&#8217;clock?&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5678.png" alt="" class="wp-image-24019" style="width:475px;height:428px" width="475" height="428" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5678.png 733w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5678-300x270.png 300w" sizes="auto, (max-width: 475px) 100vw, 475px" /></figure></div>


<h2 class="wp-block-heading"><strong>Measure and Draw Angles</strong>&nbsp;</h2>



<h3 class="wp-block-heading"><strong>Measuring angles with a protractor</strong>&nbsp;</h3>



<p>Angles are measured in <strong>degrees.</strong> The symbol for degrees is a small circle °.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5679-1024x561.png" alt="protractor" class="wp-image-24020" style="width:517px;height:283px" width="517" height="283" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5679-1024x561.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5679-300x164.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5679-768x421.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5679.png 1125w" sizes="auto, (max-width: 517px) 100vw, 517px" /></figure></div>


<p><em>Protractor</em>&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



<ul class="wp-block-list">
<li>The full circle is 360° (360 degrees).&nbsp;</li>



<li>A half-circle or a straight angle is 180°.&nbsp;</li>



<li>A quarter-circle or a right angle is 90°.&nbsp;</li>
</ul>



<h2 class="wp-block-heading"><strong>How to measure an angle with a protractor?</strong>&nbsp;</h2>



<p>A protractor is a tool that is used to measure and draw angles.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-1024x555.png" alt="How to measure an angle with a protractor? " class="wp-image-24022" style="width:663px;height:359px" width="663" height="359" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-1024x555.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-300x163.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-768x416.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680.png 1297w" sizes="auto, (max-width: 663px) 100vw, 663px" /></figure></div>


<p><em>Protractor</em>&nbsp;</p>



<ul class="wp-block-list">
<li>Place the midpoint of the protractor on the vertex of the angle.&nbsp;&nbsp;</li>



<li>Line up one side of the angle with the line zero of the protractor&nbsp;<br>(Where you see the number 0).&nbsp;</li>



<li>Read the degrees where the other side crosses the number scale.&nbsp;</li>
</ul>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5681-1024x472.png" alt="How to measure an angle with a protractor? 2" class="wp-image-24023" style="width:620px;height:286px" width="620" height="286" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5681-1024x472.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5681-300x138.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5681-768x354.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5681-1536x708.png 1536w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5681.png 1560w" sizes="auto, (max-width: 620px) 100vw, 620px" /></figure></div>


<p><strong>Example:</strong>&nbsp;</p>



<p>Draw ∠ABC=60° with a ruler and a protractor.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-1024x555.png" alt="How to measure an angle with a protractor? 3" class="wp-image-24021" style="width:536px;height:290px" width="536" height="290" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-1024x555.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-300x163.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680-768x416.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5680.png 1297w" sizes="auto, (max-width: 536px) 100vw, 536px" /></figure></div>


<ul class="wp-block-list">
<li>Draw a straight-line <em>AB</em>.&nbsp;</li>



<li>Place a dot at <em>B</em>.  This dot represents the vertex of the angle.&nbsp;</li>



<li>Place the center of the protractor at <em>B</em> and the baseline of the protractor along with the arm <em>BA</em>.&nbsp;</li>



<li>Find 60° on the scale and mark a small dot at the edge of the protractor.&nbsp;</li>



<li>Join the vertex <em>B&nbsp; </em>to the small dot with a ruler to form the second arm, <em>BC</em>, of the angle.&nbsp;</li>



<li>Mark the angle with a small arc as shown.&nbsp;</li>
</ul>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5682.png" alt="60 degree" class="wp-image-24025" style="width:497px;height:272px" width="497" height="272" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5682.png 961w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5682-300x165.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5682-768x421.png 768w" sizes="auto, (max-width: 497px) 100vw, 497px" /></figure></div>


<h3 class="wp-block-heading"><strong>Add and Subtract Angle Measures</strong>&nbsp;</h3>



<p><strong>Finding the measure of an unknown angle by using the known measures.</strong>&nbsp;</p>



<p>If ∠ABD = 107°, what is the measure of ∠ABC?&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="517" height="403" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5689.png" alt="Add and Subtract Angle Measures " class="wp-image-24033" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5689.png 517w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5689-300x234.png 300w" sizes="auto, (max-width: 517px) 100vw, 517px" /></figure></div>


<p>We know that:&nbsp;</p>



<p>∠ABC + ∠CBD = ∠ABD&nbsp;</p>



<p>Plug in the known: n + 37° = 107°&nbsp;</p>



<p>Use the inverse operation to isolate the variable n = 107° – 37° = 70°&nbsp;</p>



<p>So, ∠ABC = 70°.&nbsp;</p>



<h2 class="wp-block-heading"><strong>Exercise:</strong></h2>



<ol class="wp-block-list" type="1">
<li>Use a protractor to draw an angle measure for 65<sup>0</sup>.</li>



<li>How many 60<sup>0</sup> angles does it take to make a full turn?</li>



<li><strong>How many degrees are in a twelfth of a full turn?</strong></li>



<li>What fraction of the circle does a 120<sup>0</sup> angle turn through?</li>



<li>What are the measures of an angle?</li>



<li>What are the 5 types of angles?</li>



<li>What is a zero angle?</li>



<li>Find the following missing angles.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5692.png" alt="Find the following missing angles." class="wp-image-24037" style="width:434px;height:160px" width="434" height="160" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5692.png 528w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5692-300x111.png 300w" sizes="auto, (max-width: 434px) 100vw, 434px" /></figure></div>


<ol class="wp-block-list" start="9">
<li>Find the unknown angles from the figure below.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5694.png" alt="Find the unknown angles from the figure below." class="wp-image-24039" style="width:345px;height:151px" width="345" height="151" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5694.png 531w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5694-300x131.png 300w" sizes="auto, (max-width: 345px) 100vw, 345px" /></figure></div>


<ol class="wp-block-list" start="10">
<li>What is the value of x?</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5695.png" alt="70 degree" class="wp-image-24040" style="width:235px;height:165px" width="235" height="165" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5695.png 356w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5695-300x211.png 300w" sizes="auto, (max-width: 235px) 100vw, 235px" /></figure></div>


<h3 class="wp-block-heading"><strong>What have we learnt:</strong></h3>



<ul class="wp-block-list">
<li>To use and apply vocabulary associated with angles.</li>



<li>To identify examples of different types of angles.</li>



<li>To measure and draw angles with a protractor.</li>



<li>To understand angles and unit angles.</li>



<li>To add and subtract angle measures.</li>
</ul>



<h3 class="wp-block-heading"><strong>Concept Map:&nbsp;</strong>&nbsp;</h3>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5686-1024x539.png" alt="Concept Map:  " class="wp-image-24030" style="width:674px;height:355px" width="674" height="355" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5686-1024x539.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5686-300x158.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5686-768x404.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5686-1536x808.png 1536w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5686.png 1563w" sizes="auto, (max-width: 674px) 100vw, 674px" /></figure></div>