Question

triangle abc is an isosceles right triangle. what is the measure of one base angle? 30° 45° 60° 90°

Explanation:

Step1: Recall triangle angle sum and isosceles right triangle properties

In any triangle, the sum of interior angles is \(180^\circ\). An isosceles right triangle has one right angle (\(90^\circ\)) and two equal base angles (let each be \(x\)). So the equation is \(90^\circ + x + x = 180^\circ\).

Step2: Solve for the base angle

Simplify the equation: \(90^\circ + 2x = 180^\circ\). Subtract \(90^\circ\) from both sides: \(2x = 180^\circ - 90^\circ = 90^\circ\). Then divide by 2: \(x=\frac{90^\circ}{2}=45^\circ\).

Answer:

B. \(45^\circ\)