Question

find the measure of angle 8. 4x + 87 8x + 33

Explanation:

Step1: Identify angle - pair relationship

Assume the two lines are parallel. Angle \(4x + 87\) and angle \(8x+33\) are corresponding angles (or alternate - exterior angles if the lines are parallel), and they are equal. So we set up the equation \(4x + 87=8x + 33\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(87 = 4x+33\). Then subtract 33 from both sides: \(4x=87 - 33=54\). Divide both sides by 4: \(x = 13.5\).

Step3: Find the measure of angle \(4x + 87\)

Substitute \(x = 13.5\) into \(4x + 87\). \(4\times13.5+87=54 + 87=141\).

Step4: Use angle - pair relationship for angle 8

Angle 8 and the angle \(4x + 87\) are vertical angles. Vertical angles are equal. So the measure of angle 8 is also \(141^{\circ}\).

Answer:

\(141^{\circ}\)