Question

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

Explanation:

Step1: Identify angle - pair relationship

Angles \(4x + 87\) and \(8x+33\) are vertical angles, so they are equal.
\[4x + 87=8x + 33\]

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides:
\[87 = 4x+33\]
Subtract 33 from both sides:
\[4x=87 - 33=54\]
Divide both sides by 4:
\[x = \frac{54}{4}=13.5\]

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

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

Step4: Find the measure of angle 8

Angle 8 and the angle \(4x + 87\) are a linear - pair. A linear - pair of angles are supplementary (sum to 180°).
Let the measure of angle 8 be \(y\). Then \(y+141 = 180\).
Subtract 141 from both sides:
\[y=180 - 141 = 39\]

Answer:

39