Question

In the given figure, if AB || CD, APQ = 60° and PRD = 137°, then find the value of x and y

Answer 1

The value of xx and yy is 60\ degree60 degree and 77\ degree77 degree

Step-by-step explanation:

Given,

In figure, AB \parallel CDAB∥CD ,\angle APQ=60\ degree∠APQ=60 degree and \angle PRD=137\ degree∠PRD=137 degree

From figure,

RR is a point angle.

So, \angle R=180\ degree∠R=180 degree

⇒\angle QRP+\angle PRD=180∠QRP+∠PRD=180

⇒\angle QRP=180-137∠QRP=180−137

⇒\angle QRP=43∠QRP=43

In \triangle PQR△PQR ,

x+y+43=180x+y+43=180

⇒x+y=180-43x+y=180−43

⇒x+y=137x+y=137 __1

∵ AB \parallel CDAB∥CD , \angle APQ∠APQ and \angle PQR∠PQR alternate angles.

So, \angle APQ=\angle PQR∠APQ=∠PQR

⇒x=60\ degreex=60 degree

Plug the value in equation-1,

⇒60+y=13760+y=137

⇒y=137-60y=137−60

∴ y=77\ degreey=77 degree

So, The value of xx and yy is 60\ degree60 degree and 77\ degree77 degree

Hope it helps u .

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Answer 2

Answer:

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