Question

1. find m∠srq if m∠srd = 95°, m∠srq = 75x + 3, and m∠drq = 29x.

Explanation:

Step1: Identify angle relationship

From the diagram, \( m\angle SRQ = m\angle SRD + m\angle DRQ \). So, \( 75x + 3 = 95 + 29x \).

Step2: Solve for \( x \)

Subtract \( 29x \) from both sides: \( 75x - 29x + 3 = 95 \) → \( 46x + 3 = 95 \).
Subtract 3: \( 46x = 95 - 3 = 92 \).
Divide by 46: \( x = \frac{92}{46} = 2 \).

Step3: Find \( m\angle SRQ \)

Substitute \( x = 2 \) into \( 75x + 3 \): \( 75(2) + 3 = 150 + 3 = 153 \).

Answer:

\( 153^\circ \)