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

Given:

One angle of a triangle is equal to the sum of the other two.

To do:

 We have to show that the triangle is a right triangle.

Solution:

We know that,

Sum of the angles in a triangle is $180^o$.

Let the angles of the triangle be $x, y$ and $z$.

Let $x=y+z$

Therefore,

$x+y+z=180^o$

$x+x=180^o$

$2x=180^o$

$x=90^o$

One of the angles of the triangle is $90^o$

Therefore, the triangle is a right-angled triangle.

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Updated on: 10-Oct-2022

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