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.
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Correct Answer: Option 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
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