Question

diagram with intersecting lines at point b, angles (3x + 8)° and (5x - 40)°, points a, c (arrows up), d (arrow down), e (arrow down). multiple choice options: 56°, 80°, 90°, 24°.

Explanation:

Step1: Identify vertical angles

The angles \((3x + 8)^\circ\) and \((5x - 40)^\circ\) are vertical angles, so they are equal.
\[3x + 8 = 5x - 40\]

Step2: Solve for \(x\)

Subtract \(3x\) from both sides:
\[8 = 2x - 40\]
Add 40 to both sides:
\[48 = 2x\]
Divide by 2:
\[x = 24\]

Step3: Find the angle measure

Substitute \(x = 24\) into \((3x + 8)^\circ\):
\[3(24) + 8 = 72 + 8 = 80^\circ\]
Or into \((5x - 40)^\circ\):
\[5(24) - 40 = 120 - 40 = 80^\circ\]

Answer:

\(80^\circ\) (corresponding to the option with \(80^\circ\))