What must be true about the two non-right angles of a right triangle?

What must be true about the two non-right angles of a right triangle?

• A. Both angles are acute.
• B. One angle is acute and one is obtuse.
• C. The angles are congruent.
• D. Both angles are obtuse.

Answer: (A)

In a right triangle, one angle measures 90 degrees, which is a right angle. The sum of all angles in any triangle is always 180 degrees. This means that the remaining two angles must sum to 90 degrees as well (180 degrees minus the right angle). Since both of these angles must add up to 90 degrees, each individual angle must be less than 90 degrees. Angles that are less than 90 degrees are classified as acute angles. Therefore, both non-right angles in a right triangle are necessarily acute. This understanding of angle properties and definitions leads us to conclude that option A is the correct choice, as it accurately reflects the nature of the two non-right angles in a right triangle.

In a right triangle, one angle measures 90 degrees, which is a right angle. The sum of all angles in any triangle is always 180 degrees. This means that the remaining two angles must sum to 90 degrees as well (180 degrees minus the right angle).

Since both of these angles must add up to 90 degrees, each individual angle must be less than 90 degrees. Angles that are less than 90 degrees are classified as acute angles. Therefore, both non-right angles in a right triangle are necessarily acute.

This understanding of angle properties and definitions leads us to conclude that option A is the correct choice, as it accurately reflects the nature of the two non-right angles in a right triangle.