BdMO National Junior 2015#6

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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samiul_samin
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BdMO National Junior 2015#6

Unread post by samiul_samin » Tue Feb 19, 2019 10:48 am

$ABCD$ is a parallelogram where $\angle{ACB}=80^{\circ} $ $\angle{ACD}=20^{\circ} $ ,$P$
is a point on $AC$ such that,$\angle{ABP}=20^{\circ} $ and $Q$ is a point on $AB$ such that $\angle{ACQ}=30^{\circ} $ .Find the magnitude of the angle determined by the lines $CD$ and $PQ$.

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samiul_samin
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Re: BdMO National Junior 2015#6

Unread post by samiul_samin » Sat Feb 23, 2019 2:15 pm

Hint
Draw a new line to get some benefit.
Answer
$\angle {QRC=50^{\circ}}$
$\angle {QRD=130^{\circ}}$
Diagram
Screenshot_2019-02-23-14-12-08-1.png
Screenshot_2019-02-23-14-12-08-1.png (38.21 KiB) Viewed 853 times

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