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.
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)