Question

What is the relationship between the acute angles of a right triangle? Explain your answer.

Answer 1

The acute angles add up to 90°.

Explanation:

The sum of the interior angles of a triangle is 180°. In a right triangle has one 90° angle and two acute angles. Because the sum of the angles of a triangle must equal 180°, the two acute angles in a right triangle must equal 90°.

Answer 2

The relationship between the acute angles of a right triangle is that they ALWAYS add up to 90 degrees.

In any triangle, all the measures of the angles add up to 180 degrees.

`a+b+c=180`

Let c, be the right angle of the right triangle. This is always 90 degrees regardless of the type of right triangle.

`a+b+90=180`

If we subtract 90 from both sides of the equation, we get

`a+b=90`

Thus, the two acute angles of a right triangle always add up to 90.