Question

what is the measure of angle b? 117 63 36 56 clear my selection

Explanation:

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

Use the linear - pair relationship. If two angles form a linear pair, their sum is \(180^{\circ}\). So, \(a + 117^{\circ}=180^{\circ}\), then \(a = 180^{\circ}-117^{\circ}=63^{\circ}\).

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

Use the triangle - angle sum theorem. The sum of the interior angles of a triangle is \(180^{\circ}\). Let the 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: \(b+81^{\circ}+63^{\circ}=180^{\circ}\).

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Answer:

\(36\)