Question

find the measure of angle 8. 1 2 3 4 3x + 54 5 8 2x + 63

Explanation:

Step1: Note vertical - angle relationship

Vertical angles are equal. Angle 4 and the angle labeled \(3x + 54\) are vertical angles, and angle 8 and the angle labeled \(2x+63\) are vertical angles. Also, angle 4 and angle 8 are corresponding angles (assuming the two lines are parallel), so \(3x + 54=2x + 63\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides of the equation \(3x + 54=2x + 63\).
\(3x-2x+54=2x - 2x+63\), which simplifies to \(x+54 = 63\). Then subtract 54 from both sides: \(x=63 - 54=9\).

Step3: Find the measure of angle 8

Since angle 8 has a measure of \(2x + 63\), substitute \(x = 9\) into the expression.
\(2x+63=2\times9+63=18 + 63=81\).

Answer:

81