Question

what is the measure of angle e? *

Explanation:

Step1: Find the interior angle of a regular pentagon

The formula for the interior angle of a regular polygon is \(\frac{(n - 2)\times180^{\circ}}{n}\), where \(n\) is the number of sides. For a pentagon (\(n = 5\)), the interior angle is \(\frac{(5 - 2)\times180^{\circ}}{5}=\frac{3\times180^{\circ}}{5}=108^{\circ}\).

Step2: Find the interior angle of a regular octagon

For an octagon (\(n = 8\)), using the same formula \(\frac{(n - 2)\times180^{\circ}}{n}\), we get \(\frac{(8 - 2)\times180^{\circ}}{8}=\frac{6\times180^{\circ}}{8}=135^{\circ}\).

Step3: Calculate the measure of angle \(e\)

Since the sum of angles around a point is \(360^{\circ}\), we have \(e=360^{\circ}-108^{\circ}-135^{\circ}\).
\(e = 117^{\circ}\)

Answer:

\(117^{\circ}\)