Answer:
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.
Step-by-step 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°.
