Question

Use the diagram below to answer the following questions.

The value of x is
The measure of 1 is
The measure of 2 is
The measure of 3 is
The measure of 4 is
The measure of 5 is
The measure of 6 is
The measure of 7 is
The measure of 8 is

Answer 1

The value of x is 24. The measures of angles 1,2,3,4,5,6,7,8 are 101, 79, 101, 101, 79, 79, 89, 89 respectively.

Explanation:

If two line intersect each other, then vertical opposite angles are same.

`3x+19=5x-29` (Vertical opposite angles)

`19+29=5x-3x`

`48=2x`

Divide both sides by 2.

`24=x`

The value of x is 24.

Measure of angle 2 is

`\angle 2 =3x+7=3(24)+7=79` (Vertical opposite angles)

The measure of angle 2 is 79°.

Measure of angle 1 is

`\angle 1 =180-\angle 2=180-79=101` (Angle 1 and 2 are supplementary angles)

The measure of angle 1 is 101°.

Measure of angle 3 is

`\angle 3 =180-\angle 2=180-79=101` (Angle 3 and 2 are supplementary angles)

The measure of angle 3 is 101°.

Measure of angle 4 is

`\angle 4 =4x+5=4(24)+5=101` (Vertical opposite angles)

The measure of angle 4 is 101°.

Measure of angle 5 is

`\angle 5 =\angle 2=79` (Alternate Interior Angles)

The measure of angle 5 is 79°.

Measure of angle 6 is

`\angle 5 =\angle 6=79` (Vertical opposite angles)

The measure of angle 6 is 79°.

Measure of angle 7 is

`\angle 7 =180-(5x-29)=180-(5(24)-29)=89` (Supplementary angles)

The measure of angle 7 is 89°.

Measure of angle 8 is

`\angle 8 =\angle 7=89` (Vertical opposite angles)

The measure of angle 8 is 89°.

Answer 2

The value of x is 24
The measure of 1 is 101
The measure of 2 is 79
The measure of 3 is 101
The measure of 4 is 101
The measure of 5 is 79
The measure of 6 is 79
The measure of 7 is
The measure of 8 is