Question

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

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,

angleA + angleC= angleB …………(1)

Now, in triangle

angle A +angle B+ angle C =180°

= angle B + ( angleA + angleC) =180°

= angleB + angleB =180°…………..from(1)

=2 angleB = 180°

= angle B = 180°/2

=angleB= 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

Thank you………..

Answer 2

One angle of a triangle is equal to the sum of the other two angles (given)

To Prove: One of the angles is 900

Let x, y and z are three angles of a triangle, where

z = x + y …(1)

Sum of all angles of a triangle = 180⁰

x + y + z = 180⁰

z + z = 180⁰ (Using equation (1))

2z = 180⁰

z = 90⁰ (Proved)

Therefore, triangle is a right angled triangle.

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