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In the following figure ( not to scale),...

In the following figure ( not to scale), `/_ ADC =60^(@), /_ BAD =80^(@)` and `/_EBC = 2/_PDE`. Find `/_ APE`.
ltimg src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/PS_MATH_VIII_C16_E04_022_Q01.png" width="80%"gt

A

`60^(@)`

B

`80^(@)`

C

`120^(@)`

D

`140^(@)`

Text Solution

Verified by Experts

The correct Answer is:
c
(i) Opposite angles of a cyclic quadrilateral are supplementary
(ii) BCDE is a cyclic quadrilateral . So `/_ EDC + /_EBC =180^(@)`
(iii) ABCD is a cyclic quadrilateral. So `/_ BAD + /_ BCD =180^(@)`.
(iv) Use the above results and evaluate `/_BPD`.
(v) `/_BPD =/_APE` (vertically opposite angle )
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