Question

qs bisects ∠pqr, m∠pqs=(4y - 10)°, and m∠sqr=(2y + 10)°. find m∠pqr. 60° 20° 80° 40°

Explanation:

Step1: Set equal angles

Since QS bisects ∠PQR, m∠PQS = m∠SQR. So, \(4y - 10 = 2y + 10\).

Step2: Solve for y

Subtract \(2y\) and add 10: \(2y = 20\), so \(y = 10\).

Step3: Find m∠PQS

Substitute \(y=10\): \(4(10)-10=30^\circ\).

Step4: Calculate m∠PQR

Sum of two equal angles: \(30^\circ + 30^\circ = 60^\circ\).

Answer:

A. 60°