Question

if one angle of a triangle is equal to the sum of the other two show that the triangle is right angle​

Answer 1

Let one of the two equal angles = x

Then the third angle = x+x = 2x

We know very well that the sum of all the angles of a triangle = 180°

x+x+2x = 180°

4x = 180°

x = 45°

So the Angles are = 45°,45° and 90°.

Hence proved that it is a right angled triangle.

Answer 2

Answer:

Let the angles of triangle be x

one angles of a triangle is equal to the sum of other two so ( x+x) will be first angle

ATQ

( x +x) +x+x = 180 ( sum of all angles of triangle =180)

2x +x +x = 180

4x = 180

x = 180 / 4

x = 45°

therefore

first angle = x + x

= 45 + 45

= 90°

Second angle = 45°

third angle = 45°

one angle = 90°

Hence, prooved.