________________.

Find the measure of the missing angle x of the triangle.

Find the measure of the unknown angle in the given triangle.

Find the measure of the angle d.

In the given figure,  is the sum of _____________

The measures of two angles of a triangle are 54^o and 32^o , find the third angle.
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Can a triangle have interior angle measures as 30^o , 45^o, and 90^o ?

Can a triangle have the sides as 3 cm, 4 cm, and 6 cm?

Define the measures of angles opposite to equal sides in a triangle?

What is the measure of each angle of an equilateral triangle?

In which triangle all three sides are of equal measure?

Find the vertices of each of the figures of rotation 90⁰ counter-clockwise about the origin

Given Data:

>>From figure, the vertices of the triangle are:
B(-5,0) and E(-2,1) and G(-2, -3).
>>>let, the point (x, y) be in the space and the Angle of Rotation becomes = 90.
>>>new coordinates are:
=  (x cos - y sin , y cos + x sin)
= (x cos90 -y sin90 , y cos90 + x sin90)
= (-y, x).
* Hence, the final coordinates after rotation through 90 degrees counter clockwise are (-y, x).
>>>Similarly, for the coordinates B(-5,0) and E(-2,1) and G(-2, -3) the rotation of points through 90 degrees counter clock wise becomes:
B(0,-5) and E(3, -2) and G(3,2).
***Therefore, the coordinates of triangle B(-5,0) and E(-2,1) and G(-2, -3) after rotation through 90 degrees counter clockwise becomes  B(0,-5) and E(3, -2) and G(3,2).

Find the vertices of each of the figure of rotation 90⁰ clockwise about the origin

Given Data:
                      
* From figure, the points are K(2, -2) and U(3, 3) and T(5, 0) are the vertices of the triangle.
>>Let (x, y) be the point in the space and angle of rotation becomes = -90 degrees.
*Then, the new coordinates are :
= (x cos - y sin , y cos + x sin)
                  = (x cos(-90) -y sin(-90) , y cos(-90) + x sin(-90))
                  = (y, -x).
>>Then, the new coordinates are (y, -x).
>>>Similarly, the rotation of triangular vertices K(2, -2) and U(3, 3) and T(5, 0) through 90 degrees clockwise becomes :
                                  K(-2, -2) and U(3, -3) and T(0, -5).
*Therefore, the vertices K(2, -2) and U(3, 3) and T(5, 0) after rotation through 90 degrees clockwise becomes  K(-2, -2) and U(3, -3) and T(0, -5).

Find the vertices of each of the figure of rotation 180⁰ about the origin

Given Data:

>>From figure, the coordinates of the points w, u, x are.
>>> W(-4, -3) and U(4, 0) and X(-3, -2) are the required coordinates of a triangle.
>>Let, (x, y) be the point in the space and are rotated through 180 degrees.
Then, the new coordinates are:
=  (x cos - y sin , y cos + x sin)
= (x cos180 -y sin180 , y cos180 + xsin180)
= (-x , -y)
* Then, the new coordinates of (x, y) after rotation through 180 degrees is (-x, -y).
>>>Similarly, for  W(-4, -3) and U(4, 0) and X(-3, -2) the new coordinates are:
W(4, 3) and U(-4, 0) and (3, 2).
>>>Hence, the rotation of points W(-4, -3) and U(4, 0) and X(-3, -2) through 180 degrees becomes  W(4, 3) and U(-4, 0) and (3, 2).

What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 90^o counter-clockwise about the origin?

Given That:
                    A (-3,4) B (0, 1), C (-5, 2) are the vertices of a triangle.
>>>The vertices of a triangle are rotated through 90 degrees counter clockwise direction.
>>>Let, the point on the space be (x, y). Then Angle of Rotation  becomes 90 degrees.
>>>Hence, new coordinates are:
                                 = (x cos - y sin , y cos + x sin)
                                 = (x cos90 - y sin90 , y cos90 + x sin90)
                                 = (-y , x).
>>>Similarly, the rotation of the points  A (-3,4) B (0, 1), C (-5, 2)  becomes:
                A(-4,-3) and B(-1,0) and C(-2, -5).
***Therefore, the triangle vertices A (-3,4) B (0, 1), C (-5, 2)  after rotation through 90 degrees counter clockwise are   A(-4,-3) and B(-1,0) and C(-2, -5).

What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 180^o about the origin?

Given That:
                  A (-3,4), B(0, 1), C (-5, 2) are the points of triangle.
>>we re asked to rotate the vertices of triangle by 180 degrees.
>>>let, the point be (x, y) then the angle of rotation be 180 degrees. Then:
>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
                             = (x cos180 - y sin180 , y cos180 + x sin180)
                             = (-x , -y).
>>>Hence, any point that rotated by 180 degrees will just change the sign of the coordinates.
>>>Similarly, for triangle coordinates  A (-3,4), B(0, 1), C (-5, 2) the rotation through 180 degrees about origin becomes : A(3, -4) and B(0, -1) and C(5, -2).