What is the relationship between angle measures in a right triangle?

What is the relationship between angle measures in a right triangle?

• A. All angles are equal
• B. One angle is greater than 90 degrees
• C. One angle is equal to 90 degrees
• D. Two angles are equal

Answer: (C)

In a right triangle, one of the angles is defined to be exactly 90 degrees, which is the defining characteristic of a right triangle. This right angle is crucial because it gives the triangle its name and also allows for several important properties that apply only to right triangles, such as the Pythagorean theorem. The other two angles in the triangle must sum up to 90 degrees, making them acute angles (less than 90 degrees). Since the total measure of the angles in any triangle is always 180 degrees, having one angle equal to 90 degrees directly influences the measures of the other two angles, but the key defining feature remains that one angle must be a right angle. Understanding this relationship helps in many areas of geometry, including proofs, trigonometric ratios, and real-life applications where right triangles are prevalent.

In a right triangle, one of the angles is defined to be exactly 90 degrees, which is the defining characteristic of a right triangle. This right angle is crucial because it gives the triangle its name and also allows for several important properties that apply only to right triangles, such as the Pythagorean theorem.

The other two angles in the triangle must sum up to 90 degrees, making them acute angles (less than 90 degrees). Since the total measure of the angles in any triangle is always 180 degrees, having one angle equal to 90 degrees directly influences the measures of the other two angles, but the key defining feature remains that one angle must be a right angle.

Understanding this relationship helps in many areas of geometry, including proofs, trigonometric ratios, and real-life applications where right triangles are prevalent.