Question

Please solve q 12 ?

Answer 1

`anglePQR=112.5^@`

Explanation:

Sum of interior angles of a pentagon `=3xx180=540^@`,
given that `angleA=angleB=angleD=90^@, and angleC=angleE`,
`=> angleC=angleE=(540-3xx90)/2=135^@`,
As`angleABC=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^@`