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 | ||

2 | ||

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.