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Question -

The vertical angle of an isosceles triangle is 100°. Find its base angles.



Answer -

In ∆ABC, AB = AC and ∠A = 100°
But AB = AC (In isosceles triangle)
 
∴ ∠C = ∠B (Angles opposite to equal sides)
∠A + ∠B + ∠C = 180° (Sum of angles of a triangle)
⇒ 100° + ∠B + ∠B = 180° (∵ ∠C = ∠B)
⇒ 2∠B = 180° – 100° = 80°
∴ ∠C = ∠B = 40°
Hence ∠B = 40°, ∠C = 40°

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