In Fig. 103, PO || RS and ∠PAB = 60° and ∠ACS = 100°. Then, ∠BAC =
(a) 40°
(b) 60°
(c) 80°
(d) 50°

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Solution

Since, PQ || RS
∴ ∠PAC = ∠ACS = 100^∘ [Corresponding angles]
Now, ∠PAC = 100^∘
⇒ ∠PAB + ∠BAC = 100^∘
⇒ 60^∘ + ∠BAC = 100^∘
⇒ ∠BAC = 40^∘
Hence, the correct answer is option (a).

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In the given figure, PQ || RS. ∠PAB = 60° and ∠ACS = 100°.
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