State true or false:

PQRS is a parallelogram and $∠ 1$ and $∠ 2$ are two exterior,angles, then $∠ 1 = ∠ 2$

True

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False

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Solution

The correct option is A True
$P Q R S i s g i v e n p a r a l l e l o g r a m ∠ 1 + ∠ Q R S = 180 (L i n e a r p a i r o f a n g l e s) . . . . . . (1) ∠ 2 + ∠ S P Q = 180 (L i n e a r p a i r o f a n g l e s) . . . . . . . (2) a l s o, ∠ Q R S = ∠ S P Q (o p p o s i t e a n g l e s o f ∥ g r a m a r e e q u a l) . . . . . . . (3) ⟹ ∠ 1 + ∠ S P Q = 180 (F r o m (3) . . . . . . . . . . (4) S u b t r a c t i n g e q (2) a n d e q (4) w e g e t ⟹ ∠ 1 - ∠ 2 = 0 ⟹ ∠ 1 = ∠ 2 H e n c e p r o v e d$ \\

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