In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, ∠ SQR is 75o and ∠ QPT is 25o. Calculate the value of ∠ RST.
A. 45o B. 55o C. 25o D. 50o
Correct Answer: B
Explanation
In Δ PQT, ∠ PTQ = 25o(base ∠ s of isosceles Δ) In Δ QSR, ∠ RQS = ∠ QPT + ∠ QTP (Extr = sum of interior opposite ∠ s) ∠ RQS = 25 + 25 = 50o Also in Δ QSR, 75 + ∠ RQS + ∠ QSR = 180o (sum of ∠ s of Δ) −75 + 50 + ∠ QSR = 180 125 + ∠ QSR = 180 ∠ QSR = 180 - 125 ∠ QSR = 55o But ∠ QSR and ∠ RST are the same ∠ RST = 55o
