Question

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

Answer 1

) Let the angles of a AABC be ∠A, ∠B and ∠C.
Given, ∠A = ∠B+∠C …(i)
InMBC, ∠A+ ∠B+ ∠C-180° [sum of all angles of a triangle is 180°]…(ii)
From Eqs. (i) and (ii),
∠A+∠A = 180° ⇒ 2 ∠A = 180°
⇒ 180° /2
∠A = 90°
Hence, the triangle is a right triangle.