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