Question

what is the measure of angle b?

Explanation:

Step1: Find the measure of angle \(a\)

Use the property that adjacent angles on a straight line sum to \(180^{\circ}\). So, \(a = 180^{\circ}- 117^{\circ}\)
\(a=63^{\circ}\)

Step2: Find the measure of angle \(b\)

Use the angle - sum property of a triangle (\(90^{\circ}+81^{\circ}+a + b-(90^{\circ}+81^{\circ})=180^{\circ}\), simplified from the fact that the sum of angles in a triangle is \(180^{\circ}\)). Substitute \(a = 63^{\circ}\) into the formula \(b=180^{\circ}-90^{\circ}-81^{\circ}+90^{\circ}-63^{\circ}\) (another way: using the exterior - angle - related concept, \(b=(117^{\circ}-81^{\circ})\))
\(b = 36^{\circ}\)

Answer:

\(36^{\circ}\)