Question

PQRS is a rectangle and PR and QS are its diagonals.
Angle QOR = 62°. What is the measure of Angle PSO

A. 28°
B. 45°
C. 59°
D. 62°

With explanation pls, no irrelevant Ans.

Answer 1

Answer:

Copyright answer... helpful

Answer 2

Given:

PQRS is a rectangle and PR and QS are its diagonals.

Angle QOR = 62°

To find:

Find the measure of the angle PSO

Solution:

We know from the properties of the diagonals of a rectangle that

1) the diagonals of the rectangle are equal in length.

2) The diagonals of the rectangle bisect each other.

So now, in the triangle QOR, QO and OR are of equal lengths therefore the triangle QOR will be an isosceles triangle.

In an isosceles triangle QOR sides, OQ and OR are equal in length therefore the angles OQR and ORQ will be equal.

Now,

By using the angle sum property of a triangle

∠QOR + ∠ORQ + ∠OQR = 180°

62° + 2∠OQR = 180°

∠OQR = 59°

Now, we know that the sides QR and SP are parallel. Therefore

∠OQR = ∠OSP

Therefore ∠PSO = 59°