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Question
If one angle of a triangle is equal to the sum of other two, then the measure of that angle is ______.
Solution
If one angle of a triangle is equal to the sum of other two, then the measure of that angle is 90°.
Explanation:
Let the angles of a triangle be a, b and c. It is given that,
a = b + c
We also know that, a + b + c = 180° ......[Angle sum property of a triangle]
⇒ a + a = 180° ......[∵ b + c = a]
⇒ 2a = 180°
⇒ a = `180^circ/2`
⇒ a = 90°
Hence, the measure of that angle is 90°.
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