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Question
In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to ______.
Options
40°
80°
120°
50°
Solution
In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to 40°.
Explanation:
Let ∠R = x
PQ = QR ......(Given)
∴ ∠R = ∠P = x
Now, in ΔPOR
∠P + ∠Q + ∠R = 180° ......(Angle sum property)
⇒ x + 100° + x = 180°
⇒ 2x = 180° – 100° = 80°
⇒ x = `80^circ/2` = 40°
Thus, ∠R = 40°
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