Question

.A right triangle has one right angle and two acute angles. Without
measuring the angles, what is the sum of the measures of the two
acute angles? Explain your reasoning.

Answer 1

Answer:

90°

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°.  A right triangle has one angle that is 90°, so the sum of the other two angles much add up to 90°.  90 + 90 = 180.

Answer 2

We know that, sum of three angles of a triangle is 180°. In the case of a right angled triangle, one of the angles is always 90°. So as to satisfy the condition of sum of 3 angles to be 180°, the other two angles must be <90°, and their combined sum is 90°. Therefore, ∠1 + ∠2 = 90°.