Question

1. what is the measure of a single interior angle in a regular decagon? 32. what is the measure of a single exterior angle in a regular 72 - gon?

Explanation:

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

The formula for the measure of an interior angle \(\theta_{i}\) of a regular \(n -\)gon is \(\theta_{i}=\frac{(n - 2)\times180^{\circ}}{n}\). For a decagon (\(n = 10\)), \(\theta_{i}=\frac{(10 - 2)\times180^{\circ}}{10}\).

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Step2: Recall the formula for the measure of an exterior angle of a regular polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\). The formula for the measure of an exterior angle \(\theta_{e}\) of a regular \(n -\)gon is \(\theta_{e}=\frac{360^{\circ}}{n}\). For a \(72 -\)gon (\(n = 72\)), \(\theta_{e}=\frac{360^{\circ}}{72}\).

$$ \theta_{e}=5^{\circ} $$

Answer:

1. \(144^{\circ}\)
2. \(5^{\circ}\)