Question

Explain why the sum of the measures of the acute angles of a right triangle is$90°$.

Short answer

The sum of the measures of the acute angle of a right triangle is$90°$.

Step-by-step solution

Step 1. Given Information.

A right-angled triangle.

Step 2. Formula.

Sum of all angles of a triangle is$180°$.

Step 3. Explanation.

The sum of all the angles of a triangle is$180°$.

Let x be the measure of first acute angle of the triangle.

Let y be the measure of second acute angle of the triangle.

Calculate the sum of all the angles.

$x+y+90{}^{\circ }=180°$

Now, subtract 90 from both the sides.

$x+y+90{}^{\circ }-90{}^{\circ }=180{}^{\circ }-90°$

This gives us-

$x+y=90°$

Step 4. Conclusion.

Hence, successfully proven that the sum of acute angles of a right-angles triangle is equal to$90°$.