Question

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

Answer 1

Answer:

HOPE ITS HELPFUL TO YOU!

Answer 2

$\sf{\huge{\underline{\orange{Given :-}}}}$

• One angle of a triangle is equal to the sum of other two.

$\sf{\huge{\underline{\pink{To\:prove :-}}}}$

• The triangle is a right triangle.

$\sf{\huge{\underline{\purple{Solution :-}}}}$

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Let the angles of a triangle be,

• 1 angle = ∠P

• 2 angle = ∠Q

• 3 angle = ∠R

We have given,

One angle of a triangle is equal to the sum of other two.

∠P + ∠Q = ∠R _______{1}

We know , the sum of angles of a triangle are ,

∠P + ∠Q + ∠R = 180°______{2}

Using equation ( 1 ) in (2)

∠R + ∠R = 180°

➝ 2∠R = 180°

➝ ∠R = $\cancel{\dfrac{180}{2}}$

➝ ∠R = 90°

Hence, The triangle is a right triangle.

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