Question

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

Quality answer required with diagram.
All the best! ​

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

Answer:

Given :-

One angle = Sum of other two angles

To prove :-

It is a right angled triangle

Solution :-

Let,

1st angle - ∠A

2nd angle - ∠B

3rd angle - ∠C

---------------------

∠A + ∠B = ∠C  -- Given

---------------------

We know that,

∠A + ∠B + ∠C = 180°

→ ∠C + ( ∠A + ∠B ) = 180°

→ ∠C + ∠C = 180°

→ 2∠C = 180°

→ ∠C = 180/2

→ ∠C = 90°

∠C = 90° , Therefore the triangle is right angled.