Question

In this figure, PQRS is a rectangle. If∠RPQ = 30°, then find the value of (x+y).

Answer 1

∠RPQ = 30
∠SPR = 60
and∠SPR = ∠SQR 

ΔOQR is equilateral triangle 
∠QOR =60
∠SOR = 120

so, ∠SPR +∠SOR = 60+120=180

Answer 2

student-name Pallavi Nambiar asked in Math
Indian School
In this figure, PQRS is a rectangle. If∠RPQ = 30°, then find the value of (x+y).
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student-name Ashutosh Verma answered this
5355 helpful votes in Math, Class
Dear Student,

Please find below the solution to the asked query:


Here , We know diagonals are bisect each other and both diagonals are same in size , So

OP = OQ = OR = OS ---- ( 1 )

Given : ∠ RPQ = ∠ OPQ = 30°

In ∆POQ we know OP = OQ so from base angle theorem we get

∠ OPQ = ∠ OQP = 30°

We know all internal angle of rectangle are at 90° , So
∠ PQR = ∠ OQP + ∠ OQR = 90° , Substitute values and get

30° + x° = 90°

x = 60°

From angle sum property in triangle we get in triangle POQ :

∠ OPQ + ∠ OQP + ∠ POQ = 180°

30° + 30° + ∠ POQ = 180°

∠ POQ = 120°

And

∠ POQ = ∠ ROS ( vertically opposite angles )

120° = y

So,

x + y = 60° + 120° = 180° ( Ans )

Hope this information will help you