Answer:
x=33
Measure of angle 5=81
Measure of angle 6=99
Measure of angle 7=81
Measure of angle 8=99
Step-by-step explanation:
Angles 7 and 8 are supplementary because they share a common vertex while laying on a line.
That is the measurement of angles 7 and 8 add up to be 180.
mAngle7+mAngle8=180
(2x+15) + (3x ) =180
2x+15 + 3x =180
Combine like terms:
5x+15 =180
Subtract 15 on both sides:
5x =180-15
Simplify right hand side:
5x = 165
Divide both sides by 5:
x =165/5
Simplify right hand side:
x =33
The measure of angle 7 is 2x+15=2(33)+15=66+15=81.
The measure of angle 8 is 3x=3(33)=99.
Recall vertical angles are congruent.
5 and 7 are vertical so the measure of angle 5 is 81.
6 and 8 are vertical so the measure of angle 6 is 99.
Measure of angle 5=81
Measure of angle 6=99
Measure of angle 7=81
Measure of angle 8=99
