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Question -

The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.



Answer -

In ∆ABC,
∠A + ∠C = ∠B
 
But ∠A + ∠B + ∠C = 180° (Sum of angles of a triangle)
∴ ∠B + ∠A + ∠C = 180°
⇒ ∠B + ∠B = 180°
⇒ 2∠B = 180°
⇒ ∠B = = 90°
∴ Third angle = 90°

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