In the figure shown, $P Q ∥ R S a n d S M ∥ T N$ . Then measure of angle $α$ is

58^{\circ}

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118^{\circ}

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89^{\circ}

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91^{\circ}

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Solution

The correct option is C $89^{\circ}$
$S i n c e P Q ∥ R S ∴ ∠ R S L = ∠ P T S (C o r r e s p o n d i n g a n g l e s a r e e q u a l) \Rightarrow ∠ P T S = 29.... (1) A l s o, ∠ P T S + ∠ S T N + ∠ N T Q = 180 (A n g l e s f o r m e d b y s t r a i g h t l i n e P Q) \Rightarrow 29 + ∠ S T N + 62 = 180 [∠ N T Q = 62 (g i v e n)] \Rightarrow ∠ S T N = 180 - 91 = 89.... (2) S i n c e S M ∥ T N ∠ S T N = ∠ L S M (C o r r e s p o n d i n g a n g l e s) \Rightarrow ∠ L S M = 89 (F r o m (2)) \Rightarrow ∠ L S M = α = 89 H e n c e o p t i o n (C) i s c o r r e c t a n s w e r$

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In the figure shown, PQ∥RSandSM∥TN. Then measure of angle α is

In the figure shown, $P Q ∥ R S a n d S M ∥ T N$ . Then measure of angle $α$ is