Question

find the measure of angle 8. label optional

Explanation:

Step1: Note vertical - angle relationship

Vertical angles are equal. Angle 4 and angle 5 are vertical angles, so - 3x + 39=-7x - 41.

Step2: Solve the equation for x

Add 7x to both sides: - 3x+7x + 39=-7x+7x - 41, which simplifies to 4x + 39=-41. Then subtract 39 from both sides: 4x+39 - 39=-41 - 39, so 4x=-80. Divide both sides by 4: x = - 20.

Step3: Find the measure of angle 5

Substitute x = - 20 into the expression for angle 5: - 7(-20)-41=140 - 41 = 99.

Step4: Note the relationship between angle 5 and angle 8

Angle 5 and angle 8 are supplementary (linear - pair), so angle 5+angle 8 = 180. Let the measure of angle 8 be y. Then 99 + y=180.

Step5: Solve for the measure of angle 8

Subtract 99 from both sides: y=180 - 99 = 81.

Answer:

81