Please solve q 12 ?

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1 Answer
CW
May 13, 2018

anglePQR=112.5^@

Explanation:

enter image source here
Sum of interior angles of a pentagon =3xx180=540^@,
given that angleA=angleB=angleD=90^@, and angleC=angleE,
=> angleC=angleE=(540-3xx90)/2=135^@,
AsangleABC=90^@, => angleKBC=180-90=90^@,
given PQ bisects angleKBC, => angleQBC=(angleKBC)/2=90/2=45^@,
as angleBCD=135^@,=> angleLCD=180-135=45^@
given QR bisects angleLCD,
=> angleRCD=angleRCL=(angleLCD)/2=45/2=22.5^@,
In DeltaBQC, angleBQC=180-45-22.5=112.5^@

Hence, anglePQR=angleBQC=112.5^@

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