Question

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

Options

• an isosceles triangle

• an obtuse triangle

• an equilateral triangle

• a right triangle

Answer 1

In the given problem, one angle of a triangle is equal to the sum of the other two angles.

Thus, 

 ∠A = ∠B + ∠C   ..........(1)

Now, according to the angle sum property of the triangle

In ΔABC

        ∠A + ∠B + ∠C  = 180°

 ∠B + ∠C +∠B + ∠C  = 180°

             2(∠B + ∠C )  = 180°

                  `∠B + ∠C = (180°)/2 `

∠B + ∠C = 90°                   .........(2)

Further, using (2) in (1),

 ∠A = ∠B + ∠C 

∠A = 90°

Thus, ∠A = 90°