Question

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In APQR, PR is extended through point R to point S,
m_QRS = (4x – 15)°, m_RPQ = (x + 1), and
mZPQR = (x - 2)°. Find mZRPQ.

Answer 1

Answer: x+1 =(7)+1=8

Explanation:

Answer 2

m∠RPQ = 8°

Explanation:

m∠QRS = 4x - 15

m∠RPQ = x + 1

m∠PQR = x - 2

m∠QRS is exterior angle and m∠RPQ and m∠PQr are opposite interior angles to m∠QRS

m∠QRS = m∠RPQ + m∠PQR {Exterior angle property of triangle}

4x - 15 = x +1 + x - 2

4x - 15 = x + x + 1-2 {Combine like terms}

4x - 15 = 2x - 1 {Subtract 2x from both sides}

4x - 2x - 15 = - 1

2x - 15 = - 1 {Add 15 to both sides}

2x = -1 + 15

2x = 14 {Divide both sides by 2}

x = 14/2

x = 7

m∠RPQ = x + 1 = 7 + 1 = 8°