In the given figure, PT=QRandPT||QR and the three sides PQ=RS=TS. If ∠QPT=108°, then ∠QRS is equal to
A
1220
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B
1480
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C
1680
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D
1800
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Solution
The correct option is C1680 Given that PT=QR and PT||QR.
Thus, PQRT is a parallelogram. ⇒TR=PQ and TR||PQ ⇒TR=RS=TS
(∵PQ=RS=TS)
Therefore, ΔRST is an equilateral triangle. ⇒∠TRS=60°
Also, in a parallelogram opposite angles are equal. ∴∠QRT=∠QPT=108° ∴∠QRS=∠QRT+∠TRS =108°+60° =168°
Hence, the correct answer is option (c).