Question

what is the measure of angle h? *
your answer
0 points

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a regular pentagon (\(n = 5\)), the sum of interior angles is \((5 - 2)\times180^{\circ}=540^{\circ}\). Since it's regular, each interior angle \(A=\frac{(5 - 2)\times180^{\circ}}{5}=108^{\circ}\).

Step2: Recall the formula for the sum of interior angles of an octagon

For a regular octagon (\(n = 8\)), the sum of interior angles is \((8 - 2)\times180^{\circ}=1080^{\circ}\). Each interior angle \(B=\frac{(8 - 2)\times180^{\circ}}{8}=135^{\circ}\).

Step3: Use the angle - around - a - point property

The sum of angles around a point is \(360^{\circ}\). Let the angle \(h\) be the unknown. We know that \(h+108^{\circ}+135^{\circ}=360^{\circ}\).

Step4: Solve for \(h\)

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Answer:

\(117^{\circ}\)