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Question
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
Options
80°
40°
50°
100°
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Solution
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to 50°.
Explanation:
Given, ∆ABC such that BC = AB and ∠B = 80°
In ∆ABC, AB = BC
⇒ ∠C = ∠A ...(i) [Angles opposite to equal sides are equal]
We know that, the sum of all the angles of a triangle is 180°.
∴ ∠A + ∠B + ∠C = 180°
⇒ ∠A + 80° + ∠A = 180° ...[From equation (i)]
⇒ 2∠A = 180° – 80° = 100°
⇒ ∠A = `(100^circ)/2`
⇒ ∠A = 50°
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