1
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Question

# In the given figure if ∠ADC=110∘, then ∠ABC=

A
40
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B
50
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C
60
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D
30
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Solution

## The correct option is A 40∘We know that, the measure of the angle subtended by an arc at the center is double the measure of the angle subtended by it at any point on the remaining part of the circle. ⇒m∠AOC (major arc) =2∠ADC ⇒m∠AOC (major arc) =220∘ and m∠AOC (major arc)+m∠AOC (minor arc)=360∘ ∴m∠AOC (minor arc) =360∘−220∘=140∘ (∵m∠AOC (major arc) =220∘) Now, OABC is an inscribed quadrilateral and opposite angles of an inscribed quadrilateral are supplementary) ∴m∠AOC (minor arc) +∠ABC=180∘ ⇒∠ABC=180∘−140∘=40∘

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