Question

what is the measure of∠1 in this isosceles right triangle?
30°
45°
60°
90°

Explanation:

Step1: Recall triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\).

Step2: Use properties of isosceles right - triangle

In an isosceles right - triangle, one angle is \(90^{\circ}\). Let \(\angle1=\angle2\) (since it's isosceles). Then \(90^{\circ}+\angle1+\angle2 = 180^{\circ}\). Substituting \(\angle2=\angle1\), we get \(90^{\circ}+2\angle1 = 180^{\circ}\).

Step3: Solve for \(\angle1\)

Subtract \(90^{\circ}\) from both sides: \(2\angle1=180^{\circ}-90^{\circ}=90^{\circ}\). Divide both sides by 2: \(\angle1 = 45^{\circ}\).

Answer:

\(45^{\circ}\)