Question
Find the measure of each angle in the diagram.
- 130, 50, 130, 50
- 120, 60, 120, 60
- 156, 24, 156, 24
- 110, 70, 110, 70
Hint:
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
The correct answer is: 130, 50, 130, 50
Vertical angles are congruent, so:
10y = 7x + 4
7x – 10y = -4 --- Eq. 1
3y + 11 = 4x – 22
4x – 3y = 33 --- Eq. 2
Multiplying Eq. 1 by 4 and Eq. 2 by 7, we get
28x – 40y = -16
28x – 21y = 231
Subtracting the above two equations, we get
40y – 21 y = 231 + 16 = 247
19y = 247
y = 13
4x – 3×13 = 33
4x = 72
x = 18
Angle 1 = 10y = 130
Angle 2 = 4x – 22 = 50
Angle 3 = 130
Angle 4 = 50
Hence, the correct option is A.
Vertical angles are formed when two lines meet each other at a point. They are always equal to each other. In other words, whenever two lines cross or intersect each other, 4 angles are formed. We can observe that two angles that are opposite to each other are equal and they are called vertical angles.
Related Questions to study
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Two angles are said to be supplementary is the sum of their measures is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Two angles are said to be supplementary is the sum of their measures is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of a linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of a linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Here, sum of angles 1 and 2 is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Here, sum of angles 1 and 2 is 180°.
Which property does the statement illustrate?
Same applies on number and shapes.
Which property does the statement illustrate?
Same applies on number and shapes.
Which property does the statement illustrate?
If a=b, then b = a.
Which property does the statement illustrate?
If a=b, then b = a.
Find the measure of each angle in the diagram.
Find the measure of each angle in the diagram.
Complete the statement with <, >, or =.
If m∠ 4 = 30, then m∠ 5? m∠ 4.
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
If m∠ 4 = 30, then m∠ 5? m∠ 4.
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
m∠ 8 + m∠ 6? 150
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
m∠ 8 + m∠ 6? 150
When two angles are formed on a straight line, they are called linear pair.
What is the reason for statement 2?
| Statement | Reason | |
| 1 |  |
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| 2 |  |
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| 3 |  |
Alternate exterior angles are always equal.
What is the reason for statement 2?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Alternate exterior angles are always equal.
What is the reason for statement 3?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Corresponding angles are equal.
What is the reason for statement 3?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Corresponding angles are equal.
Solve for x.
In math, a linear pair of angles are those two adjacent angles whose sum is 180°.
Solve for x.
In math, a linear pair of angles are those two adjacent angles whose sum is 180°.
Solve for x.
When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.
Solve for x.
When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.
