Question

In a parallelogram PQRS, ∠P = 65°.Find the measure of ∠ Q , ∠ R and ∠S. Also verify your answer using angle sum property.

Answer 1

$Given \:In \: a \: parallelogram \: PQRS , \\\angle P = 65\degree$

$i) \angle P + \angle Q = 180 \degree$

$\blue{ ( \because Sum \: of \: adjacent }\\\blue{ angles\: are \: supplementary ) }$

$\implies 65\degree + \angle Q = 180 \degree$

$\implies \angle Q = 180 \degree - 65\degree$

$\implies \angle Q = 115 \degree$

$ii) \angle P = \angle R$

$\blue{ ( \because Opposite \: angles }\\\blue{ are \: equal ) }$

$\angle P = \angle R = 65\degree$

$and \: \angle S = \angle Q = 115 \degree$

Therefore.,

$\red{ Angles \: of \: parallelogram \: PQRS \:are}\\\green { \angle P = \angle R = 65\degree} \\\green { and \: \angle Q = \angle A = 115\degree}$

Verification by Angle Sum Property :

$\pink{ (Sum \: of \: the \: angles \: equals } \\\pink{ to \: 360\degree ) }$

$\angle P + \angle Q + \angle R + \angle S\\ = 65\degree + 115\degree + 65\degree + 115\degree\\\green{= 360\degree}$

•••♪