Question

if a triangle has one angle that is equal to the sum of its other two angles, what type of triangle is it?
a an isosceles triangle
b an obtuse triangle
c an acute triangle
d a right triangle

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is $180^{\circ}$. Let the three angles of the triangle be $A$, $B$, and $C$, so $A + B + C=180^{\circ}$.

Step2: Apply given condition

Given that one angle is equal to the sum of the other two. Let $A = B + C$.

Step3: Substitute and solve

Substitute $A = B + C$ into $A + B + C=180^{\circ}$, we get $A+A = 180^{\circ}$, which simplifies to $2A=180^{\circ}$. Then $A = 90^{\circ}$.

Answer:

d. a right triangle