Question

The diagonal PR and QS of a rectangle PQRS intersect each other at A. If angle RSQ=40 degree , find angle PAQ.​

Answer 1

According to the question,

PQRS is a rectangle, and A is the intersection point of diagonals PR and SQ.

So,

PR = SQ (Diagonals of a rectangle are equal])

and, RA = SA  (Diagonals of a rectangle bisect each other)

∴∠ASR =∠ARS =40°  (Angles opposite to equal sides are equal)

Thus, ∠SAR = 180° - (40 + 40)° = 180° - 80° = 100°

Now, since PR and SQ are diagonals of a rectangle.

Then, PR and SQ bisect each other at A

Thus, ∠SAR = ∠PAQ = 100° (vertical angles are equal)

Ans) ∠PAQ = 100°