Question

find the measures of the interior angles of the triangle.
∠a = 45 °
∠b = 110 °
∠c = 25 °

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles in a triangle is \(180^\circ\). Since \(\angle C\) is a right angle, \(\angle C = 90^\circ\). So, \((x + 8) + x + 90 = 180\).

Step2: Solve for \(x\)

Simplify the equation: \(2x + 98 = 180\). Subtract 98: \(2x = 82\). Divide by 2: \(x = 41\).

Step3: Find each angle

\(\angle B = x = 41^\circ\). \(\angle A = x + 8 = 41 + 8 = 49^\circ\). \(\angle C = 90^\circ\).

Answer:

\(\angle A = 49^\circ\), \(\angle B = 41^\circ\), \(\angle C = 90^\circ\)