Question

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

Answer 1

Given:-

$\angle{A} = \angle {B} +\angle {C}$

To show :-

The triangle is right angle triangle.

Solution:-

Let the angle be A, B and C respectively.

A/Q.

$\angle{A} = \angle{B} + \angle {C}$

Now,Sum of all angle of a triangle is 180°.

$\angle{A} + \angle{B}+\angle{C} = 180^{\circ}$

since, $\angle{A} = \angle{B}+\angle{C}$

Put the value of angle A.

$\angle{A} + \angle{A} = 180^{\circ}$

$2\angle{A} = 180^{\circ}$

$\angle{A} = \dfrac{180}{2}$

$\angle{A} = 90^{\circ}$

Since, the triangle whose one angle is 90° is known as right angle.

hence, it is a right angle triangle proved...

Answer 2

$\huge\bf{\green{\mid{\overline{\underline{Explained\:Answer}}}\mid}}$

$<font color = "blue">Given →</font color = "pink">$

Angle A = Angle B + Angle C

$<font color = "blue">To show →</font color = "pink">$

It is a Right Angled Triangle.

$<font color = "blue">Solution →</font color = "pink">$

Let the angle be A, B and C respectively.

According to the question:

Angle A = Angle B + Angle C

$<font color = "blue">Theorem Used →</font color = "pink">$

With the use of the theorem of sum of all the angles of a triangle is 180°.

Angle A + Angle B + Angle C = 180°

$<font color = "blue">Solve →</font color = "pink">$

Angle A + Angle B + Angle C = 180°

°.° Angle A = Angle B + Angle C

By putting the value of angle A:

=> Angle A + Angle A = 180°

=> 2 (Angle A) = 180°

=> Angle A = 180° / 2

=> Angle A = 90°

$<font color = "blue">Hence Proved →</font color = "pink">$

.°. It is a Right Angled Triangle.