Question

Prove that if one angle of a triangle is equal to the sum of the other two angles,
the triangle is right angled.​

Answer 1

Answer:

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Sum of all angles in a triangle iis 180°

One angle in right angled triangle is 90°

hence sum of other two angles is 90°

Answer 2

Answer:

Given

One angle of triangle is equal to sum of other two angles.

To Prove

if one angle of a triangle is equal to the sum of the other two angles, then the triangle is right angled.

Solution

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

According to question

One angle of triangle is equal to sum of other two angles

Thus, we can say x = y+z -----(1)

(you can also take y = x+z or z = x+y)

As we know sum of angles of triangle is 180 degree

implies x+y+z = 180 degree -----(2)

Substituting (1) in (2) we get

x+x = 180

2x = 180

x = 180/2

x = 90

As one angle of triangle i.e x is 90 degree implies that the triangle is right angled.

Hope it helps you.

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