Question

b 81° a 117°

Explanation:

Step1: Find the value of \(a\)

Use the property that the sum of an interior angle and its adjacent exterior angle is \(180^{\circ}\). So \(a + 117^{\circ}=180^{\circ}\), then \(a = 180^{\circ}-117^{\circ}=63^{\circ}\)

Step2: Find the value of \(b\)

Use the triangle - angle sum property (the sum of angles in a triangle is \(180^{\circ}\)). Given one angle is \(90^{\circ}\) (right - angle) and \(a = 63^{\circ}\), then \(b+90^{\circ}+a = 180^{\circ}\). Substitute \(a = 63^{\circ}\) into the equation: \(b+90^{\circ}+63^{\circ}=180^{\circ}\), \(b=180^{\circ}-(90^{\circ} + 63^{\circ})=27^{\circ}\)

Answer:

\(a = 63^{\circ}\), \(b = 27^{\circ}\)