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

2014 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
CEMC Gauss (Grade 8)

Page

Toolbox

Search

2014 CEMC Gauss (Grade 8) Problems/Problem 4

Problem

Solution