In a right triangle, the two acute angles sum to how many degrees?

In a right triangle, the two acute angles sum to how many degrees?

• A. The two acute angles in a right triangle sum to 180 degrees.
• B. The two acute angles in a right triangle sum to 90 degrees.
• C. All three interior angles sum to 360 degrees.
• D. The right angle plus one acute angle equals 90 degrees.

Answer: (B)

In any triangle, the interior angles add up to 180 degrees. A right triangle has one angle measuring 90 degrees, so the other two angles must sum to 180 − 90 = 90 degrees. Those two angles are the acute angles, and since they add to 90, they are complementary. That’s why the two acute angles in a right triangle total 90 degrees. (They can’t sum to 180, which would leave no room for the third angle, and 90 plus an acute angle isn’t 90 since the acute angle is positive.)

In any triangle, the interior angles add up to 180 degrees. A right triangle has one angle measuring 90 degrees, so the other two angles must sum to 180 − 90 = 90 degrees. Those two angles are the acute angles, and since they add to 90, they are complementary. That’s why the two acute angles in a right triangle total 90 degrees. (They can’t sum to 180, which would leave no room for the third angle, and 90 plus an acute angle isn’t 90 since the acute angle is positive.)