In Fig. 14.113, PQRS is a rhombus in which the diagonal PR is produced to T. If ∠SRT=152°, find x,y and z.

Question

In Fig. 14.113, PQRS is a rhombus in which the diagonal PR is produced to T. If &#x2220; SRT=152&#xB0;, find x,y and z.

Philoid · Accepted Answer

Given,

PQRS is a rhombus

∠SRT = 152°

We know that diagonals of a rhombus bisects each other at 90°

Hence , ∠SOR = 90° = y = 90°

∠SRT+∠SRO= 180° (linear pair of angles)

= 152°+∠SRO = 180°

∠SRO = 180° -152°= 28°

NOW , ∠SRO = z ∵SR=SP

= z = 28°

And , ∠RSO+∠SRO + y = 180° (angle sum property of triangle)

= ∠RSO+28°+90°= 180°

= ∠RSO = 180°-118° = 62°

= ∠X = ∠RSO = 62° (alternate angles)