Question

1. if m∠1 = 11x + 5 and m∠2 = 8x − 15, find m∠2. options: 75, 115, 10, 65

Explanation:

Step1: Identify angle relationship

Angles 1 and 2 are supplementary (form a straight line), so \( m\angle1 + m\angle2 = 180^\circ \).
Substitute \( m\angle1 = 11x + 5 \) and \( m\angle2 = 8x - 15 \):
\( (11x + 5) + (8x - 15) = 180 \)

Step2: Solve for \( x \)

Combine like terms:
\( 19x - 10 = 180 \)
Add 10 to both sides:
\( 19x = 190 \)
Divide by 19:
\( x = 10 \)

Step3: Find \( m\angle2 \)

Substitute \( x = 10 \) into \( m\angle2 = 8x - 15 \):
\( m\angle2 = 8(10) - 15 = 80 - 15 = 65 \)

Answer:

65