Geometry Practice Test 4

Let x, y, z be the three angles of a triangle.
∠x +∠y +∠z = 180° ......(i)
and ∠x +∠y = ∠z
Substituting in equation (i),
∠x +∠y +∠x +∠y = 180°
2(∠x +∠y) = 180°
∠x + ∠y = $\frac{180°}{2}$ = 90°
∠x +∠y = 90°
∠z = 90°
⇒ If one angle of the triangle is equal to the sum of the other two angles, then the triangle is a right angle triangle.