Question

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

Answer 1

Answer:

one angle x and other angle y

Step-by-step explanation:

x+y is the angle equal to the sum of other 2.

x+y+x+y =180degree

2(x+y) =180degree

x+y=180/2

x+y=90 degree.

so one angle is equal to 90 degree .

so the triangle is a right angled triangles

Answer 2

Step-by-step explanation:

Given:-

one angle of a triangle is equal to the sum of other two angles

To prove:-

show that the triangle is a right-angled triangle.

Proof:-

Let Consider a triangle ABC

Let angle A is the sum of other two angles B and C

=>angle A=angle B + angle C-------(1)

And we know that

The sum of the three interior angles is 180°

angle A+angle B+angle C=180°

from (1)

=>angle A+angle A=180°

=>2(angle A)=180°

=>angle A =180°/2

=>angle A=90°

and angle B+angle C=90°

It is clear that it is a right angled triangle

Hence, Proved.

Right angled triangle:-

an angle is equal to 90° of a triangle is called a right angled triangle.