Question

PQRS is a rectangle, find the angles marked x and y. *see figure above* PLS SOLVE THIS STEP BY STEP AND I'LL MARK AS BRAINLIEST!!​

Answer 1

Answer:

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Answer 2

Given: Rectangle PQRS with O as mid-point of diagonals PR and QS.

To Find: ∠x and ∠y

Solution:

• First we will consider ΔPOQ.

1. As diagonals of a rectangle bisect each other at the mid-point

⇒ OP=OQ

⇒ΔPOQ is isosceles

⇒∠OPQ=∠OQP= 24°    (1)            (angles opposite to equal sides are equal)

As we know, all angles of a triangle add up to 180°,

∴ ∠OPQ + ∠x + ∠ OQP = 180°                            

⇒ ∠x + 48° = 180°                         (from 1)

⇒∠x = 132°

• Now we will solve for ∠y using parallel line rules.

In given figure, PS║QR                (sides of a rectangle)

∴∠RPQ = ∠PRS = 24°                 (alternate interior angle)

⇒∠y = 90° - 24°= 66°                    (angle of rectangle)

⇒∠y = 66°

Hence ∠x = 132° and ∠y= 66°.