Question

what is the measure of angle a in this triangle?

Explanation:

Step1: Recall triangle - angle sum property

The sum of interior angles of a triangle is 180°. In the given right - triangle, one angle is 90° and assume the other non - right angle is 45° (since it is an isosceles right - triangle as indicated by the equal side markings). Let angle A be the unknown non - right angle.
Let the right angle = 90°, and assume the other non - right angle is x. Then, by the angle - sum property of a triangle: $\angle A+x + 90^{\circ}=180^{\circ}$.
Since the triangle has two equal sides, the non - right angles are equal. So, $\angle A=(180^{\circ}-90^{\circ})\div2$.

Step2: Calculate angle A

$\angle A=\frac{180^{\circ}-90^{\circ}}{2}=\frac{90^{\circ}}{2}=45^{\circ}$

Answer:

$45^{\circ}$