Question

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

Answer 1

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

i.e, `∠ B=∠ A+∠C` 

Now, in ΔABC 

(Sum of all aangles of triangle `180^@`) 

`∠ A+∠B+∠ C=180^@` 

`∠ B+∠ B=180^@`                       [∵ ∠ B=∠ A+∠ C]

 `2∠ B=180^@` 

`∠ B=180^@/2` 

`∠ B=90^@` 

∴ABC is a right angled a triangle