2014 CEMC Gauss (Grade 8) Problems/Problem 4

Problem

In a right-angled triangle, the measure of one angle is $55^{\circ}$ . The measure of the smallest angle in this triangle is

$\textbf{(A)}\ 1^{\circ} \qquad\textbf{(B)}\ 25^{\circ} \qquad\textbf{(C)}\ 45^{\circ} \qquad\textbf{(D)}\ 35^{\circ} \qquad\textbf{(E)}\ 90^{\circ}$

Solution

Let $x$ be the measure of the measure of the acute angle that isn't given in the problem. Since the sum of the measurements of the acute angles in the interior of a right triangle is $90^{\circ}$ , we have:

$x + 55^{\circ} = 90^{\circ}$

Thus, $x = 35^{\circ}$ .

$35^{\circ}$ is smaller than the measurement of the other acute angle, which is $55^{\circ}$ , so the answer is $\boxed{\textbf {(D) } 35^{\circ}}$ .

~anabel.disher

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2014 CEMC Gauss (Grade 8) Problems/Problem 4

Problem

Solution