If two adjacent angles of a parallelogram are in the ratio of $2 : 3$ find all the angles of the parallelogram.

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Solution

$L e t p a r a l l e l o g r a m b e P Q R S T w o a d j a c e n t a n g l e s o f p a r a l l e l o g r a m a r e i n r a t i o 2 : 3 L e t ∠ P = 2 x ∠ Q = 3 x ∠ P + ∠ Q = 2 x + 3 x = 5 x 180 = 5 x x = \frac{180}{5} = 36 ∠ P = 2 x = 2 \times 36 = 72 ∠ Q = 3 x = 3 \times 36 = 108 ∠ P = ∠ R (o p p o s i t e a n g l e s) ∠ R = 72^{0} ∠ Q a n d ∠ S a r e e q u a l ∠ S = 108^{0} ∴ a n g l e s o f p a r a l l e l o g r a m a r e 72^{0}, 108^{0}, 72^{0} a n d 108^{0}$

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