Question

1. ∠1 and ∠2 are vertical angles. if m∠1 = 17x + 1 and m∠2 = 20x − 14, find m∠2

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle1 = m\angle2 \).
\( 17x + 1 = 20x - 14 \)

Step2: Solve for \( x \)

Subtract \( 17x \) from both sides:
\( 1 = 3x - 14 \)
Add 14 to both sides:
\( 15 = 3x \)
Divide by 3:
\( x = 5 \)

Step3: Find \( m\angle2 \)

Substitute \( x = 5 \) into \( m\angle2 = 20x - 14 \):
\( m\angle2 = 20(5) - 14 \)
\( m\angle2 = 100 - 14 \)
\( m\angle2 = 86 \)

Answer:

\( 86 \)