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Question
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is ______.
Options
an isosceles triangle
an obtuse triangle
an equilateral triangle
a right triangle
Solution
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle.
Explanation:
Given, Let angle of triangle ABC be ∠A, ∠B and ∠C
Given that: ∠A = ∠B + ∠C ...(i)
We know that in any triangle ∠A + ∠B + ∠C = 180° ...(ii)
From equation (i) and (ii), get:
∠A + ∠A = 180°
2∠A = 180°
`∠A = (180^circ)/2`
∠A = 90°
Hence, the triangle is a right triangle.
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