Question

determine the measure of one of its angles. 144° 162° 1,440° 1,800°

Explanation:

Step1: Use the formula for the sum of interior angles

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 12 - sided polygon (\(n = 12\)), the sum of interior angles is \((12- 2)\times180^{\circ}=10\times180^{\circ} = 1800^{\circ}\). But we need the measure of one interior angle.

Step2: Use the formula for one interior angle of a regular polygon

The formula for one interior angle of a regular polygon is \(\frac{(n - 2)\times180^{\circ}}{n}\). Substitute \(n = 12\) into the formula: \(\frac{(12 - 2)\times180^{\circ}}{12}=\frac{10\times180^{\circ}}{12}\).
First, calculate \(10\times180^{\circ}=1800^{\circ}\), then \(\frac{1800^{\circ}}{12}=150^{\circ}\). Wait, maybe there is a mistake in the problem - reading. If we assume it's a 10 - sided polygon (since \(1440^{\circ}\) is the sum of interior angles of a 10 - sided polygon \((n-2)\times180=(10 - 2)\times180 = 1440\)), and for one interior angle of a regular 10 - sided polygon:

Step3: Calculate one interior angle of a regular 10 - sided polygon

Using the formula \(\frac{(n - 2)\times180^{\circ}}{n}\), with \(n = 10\). \(\frac{(10 - 2)\times180^{\circ}}{10}=\frac{8\times180^{\circ}}{10}\).
\(8\times180^{\circ}=1440^{\circ}\), and \(\frac{1440^{\circ}}{10}=144^{\circ}\)

Answer:

144°