Question

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

Explanation:

Step1: Calculate the interior angle of a regular pentagon

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

Step2: Calculate the interior angle of a regular decagon

For a decagon (\(n = 10\)), using the formula \(\frac{(n - 2)\times180^{\circ}}{n}\), we get \(\frac{(10 - 2)\times180^{\circ}}{10}=144^{\circ}\).

Step3: Use the angle - sum property around a point

The sum of angles around a point is \(360^{\circ}\). Let the measure of angle \(g\) be \(x\). Then \(x+108^{\circ}+144^{\circ}=360^{\circ}\).

Step4: Solve for \(x\)

\(x=360^{\circ}-(108^{\circ}+144^{\circ})\).
\(x = 360^{\circ}-252^{\circ}\).
\(x = 108^{\circ}\).

Answer:

\(108^{\circ}\)