Question

question 6: point s is in the interior of ∠pqr. if m∠sqr = 52°, m∠pqs = 3x, and m∠rqp = 8x - 8, determine the value of x. show your algebraic thinking to earn full credit.

Explanation:

Step1: Apply Angle Addition Postulate

Since point \( S \) is in the interior of \( \angle PQR \), we know that \( m\angle PQR = m\angle PQS + m\angle SQR \). Substituting the given angle measures, we get \( 8x - 8 = 3x + 52 \).

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 8x - 3x - 8 = 52 \), which simplifies to \( 5x - 8 = 52 \). Then add 8 to both sides: \( 5x = 52 + 8 \), so \( 5x = 60 \). Finally, divide both sides by 5: \( x = \frac{60}{5} = 12 \).

Answer:

\( x = 12 \)