Question

triangle sum
what is the measure of angle b?
81°
117°

Explanation:

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

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

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

Use the triangle - angle sum property (the sum of angles in a triangle is \(180^{\circ}\)). Let the three angles of the triangle be \(b\), \(81^{\circ}\), and \(a\). We know \(a = 63^{\circ}\). Then \(b+81^{\circ}+a = 180^{\circ}\), substitute \(a = 63^{\circ}\) into the equation: \(b+81^{\circ}+63^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(b + 144^{\circ}=180^{\circ}\).
Solve for \(b\): \(b=180^{\circ}-144^{\circ}=36^{\circ}\).

Answer:

\(36^{\circ}\)