Question

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

Answer 1

Let ABC be any triangle

In which measure of angleB is equal to the measure of remaining angles that is angleA and angleC

So, in triangle ABC,

angle A + angle C= angle B …………(1)

Now, in triangle

angle A +angle B+ angle C =180°

= angle B + ( angleA + angleB) =180°

= angleB + angleB =180°………….. from(1)

=2 angleB = 180°

= angle B = 180°/2

=angle B= 90°

So, one angle of triangleABC is 90° or if one angle of triangle is 90° this triangle is known as right angled triangle.

So, it is right angled triangle