In the figure both RISK and CLUE are parallelograms. Find the value of x in degrees.

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Solution

$I n t h e p a r a l l e l o g r a m R I S K, w e h a v e ∠ R l S = ∠ R K S = 120 [o p p . a n g l e s o f p a r a l l e l o g r a m a r e e q u a l)$

$A l s o, ∠ O I C = 180 ∠ R l S [L i n e a r p a i r o f a n g l e s) ⟹ O I C = 180120 = 60...... (1)$
$I n t h e p a r a l l e l o g r a m C L U E, C E ∥ L U a n d a t r a n s v e r s a l C L i n t e r s e c t s t h e m . ∠ I C O = ∠ C L U [C o r r e s p o n d i n g a n g l e s a r e e q u a l) ⟹ ∠ I C O = 70...... (2)$
$I n O I C, b y a n g l e s u m p r o p e r t y, w e h a v e ∠ I O C + ∠ O I C + ∠ I C O = 180 [F r o m (1) a n d (2)] ⟹ ∠ I C O + 60 + 70 = 180 ⟹ ∠ I O C = 1806070 = 50. ∴ x = ∠ I O C = 50^{o} [V e r t i c a l l y o p p o s i t e a n g l e s a r e e q u a l)$

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