1999 CEMC Gauss (Grade 7) Problems/Problem 6

Problem

In $\Delta ABC$ , $\angle B = 72^{\circ}$ . What is the sum, in degrees, of the other two angles?

$\text{(A)}\ 144 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 108 \qquad \text{(D)}\ 110 \qquad \text{(E)}\ 288$

Let x and y be the other two angles of the triangle.

The sum of the interior angles in a triangle is always $180^{\circ}$ , so we have:

$x + y + 72^{\circ} = 180^{\circ}$

Subtracting $72^{\circ}$ from both sides of the equation gives:

$x + y = \boxed{\textbf{(C)} 108}$