    Question

# In the given figure, ∠A=60∘ and ∠ABC=80∘, then ∠DPC and ∠BQC are respectively ___. A

30o

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B

40o

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C

20o

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D

50o

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Solution

## The correct option is C 20o In a cyclic quadrilateral, exterior angle is equal to opposite interior angle. So, in cyclic quadrilateral ABCD, we have, ∠PDC=∠ABC and ∠DCP=∠A ∠PDC=80∘ and ∠DCP=60∘ [Given, ∠ABC=80∘ and ∠A=60∘ ] In ΔDPC, we have ∠DPC=180∘−(∠PDC+∠DCP) ⇒∠DPC=180∘−(80∘+60∘)=40∘ Similarly, we have ∠QBC=∠ADC and ∠BCQ=∠BAD [∠ADC+∠ABC=180∘ (Opposite angle sum of cyclic quadrilateral), ∠ABC=80∘ and ∠A=60∘] ∠QBC=180∘−∠ABC ∠QBC=180∘−80∘=100∘ and ∠BCQ=∠BAD=60∘ Now, in ΔBQC, we have ∠BQC=180∘−(∠QBC+∠BCQ) ⇒∠BQC=180∘−(100∘+60∘)=20∘  Suggest Corrections  0      Similar questions  Related Videos   Circles and Quadrilaterals - Theorem 11
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