Question

problem 11: (first taught in lesson 30) find the measures of the angles of a right triangle with congruent acute angles. after you enter your answer press go.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. In a right - triangle, one angle is 90°.

Step2: Let the acute angles be \(x\)

Let the two congruent acute angles each be \(x\). Then the equation for the sum of the angles of the triangle is \(90 + x+x=180\).

Step3: Solve the equation

Combining like terms gives \(90 + 2x=180\). Subtract 90 from both sides: \(2x=180 - 90=90\). Divide both sides by 2: \(x = 45\). So the angles are 90°, 45°, 45°.

Answer:

90°, 45°, 45°