Question

a decagon has 10 sides. one angle of a regular decagon measures (8w + 17)°. determine the value of w. round to the nearest whole number.
options:
w = 144
w = 23
w = 16
w = 8

Explanation:

Step1: Recall the formula for the interior angle of a regular polygon

The formula for the interior angle of a regular polygon with \(n\) sides is \(\frac{(n - 2)\times180^{\circ}}{n}\). For a decagon (\(n = 10\)), the interior angle is \(\frac{(10 - 2)\times180^{\circ}}{10}=144^{\circ}\).

Step2: Set up the equation

We are given that the measure of one angle is \((8w + 17)^{\circ}\). So, we set up the equation \(8w+17 = 144\).

Step3: Solve the equation for \(w\)

Subtract 17 from both sides: \(8w=144 - 17\), so \(8w = 127\). Then divide both sides by 8: \(w=\frac{127}{8}=15.875\approx16\).

Answer:

\(w = 16\)