Question

find the measure of angle 8

Explanation:

Step1: Identify angle - relationship

Assume the angles -2x + 106 and 5x - 27 are corresponding angles (or some other equal - angle relationship based on parallel lines and transversals). Set them equal: -2x + 106=5x - 27.

Step2: Solve for x

Add 2x to both sides: 106 = 5x+2x - 27, so 106 = 7x - 27. Then add 27 to both sides: 106 + 27=7x, 133 = 7x. Divide both sides by 7: x = 19.

Step3: Find the measure of the related angle

Substitute x = 19 into -2x + 106. We get -2×19 + 106=-38 + 106 = 68.

Step4: Find the measure of angle 8

Assume angle 8 and the angle -2x + 106 are vertical angles (vertical angles are equal). So the measure of angle 8 is also 68.

Answer:

68