Question

1. if m∠pqs = 16°, m∠sqr = (9x + 17)°, and m∠pqr = (12x - 6)°, find m∠pqr

Explanation:

Step1: Use angle addition postulate

From the diagram, \( \angle PQR = \angle PQS + \angle SQR \). So we substitute the given angle measures:
\( 12x - 6 = 16 + 9x + 17 \)

Step2: Simplify the equation

Combine like terms on the right side:
\( 12x - 6 = 9x + 33 \)

Step3: Solve for x

Subtract \( 9x \) from both sides:
\( 12x - 9x - 6 = 33 \)
\( 3x - 6 = 33 \)

Add 6 to both sides:
\( 3x = 33 + 6 \)
\( 3x = 39 \)

Divide both sides by 3:
\( x = \frac{39}{3} = 13 \)

Step4: Find \( m\angle PQR \)

Substitute \( x = 13 \) into \( m\angle PQR = (12x - 6)^\circ \):
\( 12(13) - 6 = 156 - 6 = 150 \)

Answer:

\( 150^\circ \)