Question

In □PQRS side PQ∥ side RS. If m∠P = 108degree

and m∠R = 53degree

, then find m∠Q and m∠S.​

Answer 1

EXPLANATION.

In a quadrilateral PQRS.

⇒ PQ ║ RS.

⇒ m∠P = 108°.

⇒ m∠R = 53°.

As we know that,

⇒ ∠P = ∠R

⇒ ∠Q = ∠S.

⇒ ∠P + ∠Q = 180°.

⇒ 108° + ∠Q = 180°.

⇒ ∠Q = 180° - 108°.

⇒ ∠Q = 72°.

⇒ ∠R + ∠S = 180°.

⇒ 53° + ∠S = 180°.

⇒ ∠S = 180° - 53°.

⇒ ∠S = 127°.

⇒ m∠Q = 72° & m∠S = 127°.

Answer 2

Given :-

In □PQRS side PQ∥ side RS. If m∠P = 108degree

and m∠R = 53degree

To Find :-

m∠Q and m∠S.​

Solution :-

According to angle sum property

$\sf \angle Q = 180 - \angle P$

$\sf \angle Q = 180 - 108$

$\sf\angle Q = 72^{\circ}$

For angle S

$\sf \angle S = 180 - \angle R$

$\sf \angle S = 180-53$

$\sf \angle S = 127^{\circ}$