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If one angle of a triangle is equal t...

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.

Text Solution

Verified by Experts

Let,
1st angle /_A
2nd angle
angle B
3rd angle `/_C
/_A + /_B = /_C` -- Given
We know that,
`/_A + /_B + /_C = 180^@`
`/_C + ( /_A + /_B ) = 180^@`
`/_C + /_C = 180^@`
`2/_C = 180^@`
`/_C = 180/2`
`/_C = 90^@`
`/_C = 90^@`, Therefore the triangle is right angled.
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