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

Options

A. an isosceles triangle
B. an obtuse triangle
C. an equilateral triangle
D. a right triangle

Answer

D

Explanation

Let the angles of a `DeltaABC be /_A, /_B and /_C`.
Given, `" " /_A = /_B + /_C" "` …(i)
In `DeltaABC , " " /_A + /_B +/_C = 180^(@)" " ["sum of all angles of a triangle is "180^(@)`] ….(ii)
From Eqs. (i) and (ii) ,
`/_ A + /_A 180^(@)`
`implies " " 2/_A = 180^(@)`
`implies " " /_A = 180^(@) /2`
`:. " " /_A = 90^(@)`
"Hence, the triangle is a right triangle".