∠A is an obtuse angle. The measure of ∠A and twice its supplementary differ by 30°. Then ∠A can be
(a) 150°
(b) 110°
(c) 140°
(d) 120°

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Solution

Supplementary of ∠A = 180^∘ − ∠A
Now,
∠A + 30^∘ = 2(180^∘ − ∠A)
⇒ ∠A + 30^∘ = 360^∘ − 2∠A
⇒ 3∠A = 360^∘ − 30^∘
⇒ 3∠A = 330^∘
⇒ ∠A = 110^∘
Hence, the correct answer is option (b).

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∠A is an obtuse angle. The measure of ∠A and twice its supplementary differ by 30°. Then ∠A can be (a) 150° (b) 110° (c) 140° (d) 120°

Supplementary of ∠A = 180∘ − ∠A Now, ∠A + 30∘ = 2(180∘ − ∠A) ⇒ ∠A + 30∘ = 360∘ − 2∠A ⇒ 3∠A = 360∘ − 30∘ ⇒ 3∠A = 330∘ ⇒ ∠A = 110∘ Hence, the correct answer is option (b).

∠A is an obtuse angle. The measure of ∠A and twice its supplementary differ by 30°. Then ∠A can be
(a) 150°
(b) 110°
(c) 140°
(d) 120°

Supplementary of ∠A = 180^∘ − ∠A
Now,
∠A + 30^∘ = 2(180^∘ − ∠A)
⇒ ∠A + 30^∘ = 360^∘ − 2∠A
⇒ 3∠A = 360^∘ − 30^∘
⇒ 3∠A = 330^∘
⇒ ∠A = 110^∘
Hence, the correct answer is option (b).