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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
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Solution
In the given problem, one angle of a triangle is equal to the sum of the other two angles.
Thus,
∠A = ∠B + ∠C ..........(1)
Now, according to the angle sum property of the triangle
In ΔABC
∠A + ∠B + ∠C = 180°
∠B + ∠C +∠B + ∠C = 180°
2(∠B + ∠C ) = 180°
`∠B + ∠C = (180°)/2 `
∠B + ∠C = 90° .........(2)
Further, using (2) in (1),
∠A = ∠B + ∠C
∠A = 90°
Thus, ∠A = 90°
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