Question

1. a triangle is a right isosceles triangle. find the measure of each of its acute angles.

Explanation:

Step1: Recall triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). In a right - isosceles triangle, one angle is \(90^{\circ}\). Let the measure of each acute angle be \(x\).

Step2: Set up the equation

Using the angle - sum property: \(90 + x+x=180\).
Simplify the equation: \(90 + 2x=180\).
Subtract \(90\) from both sides: \(2x=180 - 90\), so \(2x = 90\).
Divide both sides by \(2\): \(x=\frac{90}{2}=45\).

Answer:

Each acute angle measures \(45^{\circ}\).