One angle of a triangle has a measure of $75 ^ { \circ }$ and the measures of the other two angles are in a ratio of 2 to 3. Find the measures of the other two angles.
A) $42 ^ { \circ }$ and $63 ^ { \circ }$
B) $44 ^ { \circ }$ and $61 ^ { \circ }$
C) $46 ^ { \circ }$ and $61 ^ { \circ }$
D) $44 ^ { \circ }$ and $590$
E) $46 ^ { \circ }$ and $590$

Question

Quizplus · Accepted Answer

The sum of angles in a triangle is $180^\circ$. Subtracting the given angle, $180^\circ - 75^\circ = 105^\circ$ is left for the other two angles. With their ratio being 2:3, their measures are $2x$ and $3x$, respectively. Solving $2x + 3x = 105^\circ$ gives $5x = 105^\circ$, so $x = 21^\circ$. Thus, the measures are $42^\circ$ and $63^\circ$.

One Angle of a Triangle Has a Measure Of 75∘75 ^ { \circ }75∘

One Angle of a Triangle Has a Measure Of $75 ^ { \circ }$