Question

1. ∠u and ∠w are vertical angles. if m∠u = 6x + 11 and m∠w = 10x − 9, find m∠u.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle U = m\angle W \). Thus, \( 6x + 11 = 10x - 9 \).

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 11 = 4x - 9 \).
Add 9 to both sides: \( 20 = 4x \).
Divide by 4: \( x = 5 \).

Step3: Find \( m\angle U \)

Substitute \( x = 5 \) into \( m\angle U = 6x + 11 \):
\( m\angle U = 6(5) + 11 = 30 + 11 = 41 \).

Answer:

\( 41^\circ \)