Question

in the right triangle, find the measure of ∠c.

Explanation:

Step1: Recall triangle angle sum

In a triangle, the sum of angles is \(180^\circ\). For a right triangle, one angle is \(90^\circ\) (angle \(B\) here).

Step2: Identify known angles

We know \(\angle A = 25^\circ\) and \(\angle B = 90^\circ\). Let \(\angle C = x\).

Step3: Apply angle sum formula

Using \(\angle A + \angle B + \angle C = 180^\circ\), substitute values: \(25^\circ + 90^\circ + x = 180^\circ\).

Step4: Solve for \(x\)

Simplify: \(115^\circ + x = 180^\circ\). Subtract \(115^\circ\) from both sides: \(x = 180^\circ - 115^\circ = 65^\circ\).

Answer:

\(65^\circ\)