Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.
match the properties to the regular polygons they describe.
an interior angle measures 150°.
an exterior angle measures 24°.
the sum of the interior angles is 2520°.
an interior angle measures 160°.
the sum of the exterior angles is 180°.
the sum of the interior angles is 2160°.
15 - gon
16 - gon
12 - gon
18 - gon
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Explanation:

Step1: Recall the formula for the sum of interior angles

The sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides.
For a 15 - gon: \(S=(15 - 2)\times180^{\circ}=13\times180^{\circ}=2340^{\circ}\). The measure of an interior angle of a regular polygon is \(A=\frac{(n - 2)\times180^{\circ}}{n}\). For \(n = 15\), \(A=\frac{(15 - 2)\times180^{\circ}}{15}=\frac{13\times180^{\circ}}{15}=156^{\circ}\). The measure of an exterior angle of a regular polygon is \(E=\frac{360^{\circ}}{n}\). For \(n = 15\), \(E=\frac{360^{\circ}}{15} = 24^{\circ}\).

Step2: For a 16 - gon

The sum of interior angles \(S=(16 - 2)\times180^{\circ}=14\times180^{\circ}=2520^{\circ}\). The measure of an interior angle \(A=\frac{(16 - 2)\times180^{\circ}}{16}=\frac{14\times180^{\circ}}{16}=157.5^{\circ}\). The measure of an exterior angle \(E=\frac{360^{\circ}}{16}=22.5^{\circ}\).

Step3: For a 12 - gon

The sum of interior angles \(S=(12 - 2)\times180^{\circ}=10\times180^{\circ}=1800^{\circ}\). The measure of an interior angle \(A=\frac{(12 - 2)\times180^{\circ}}{12}=\frac{10\times180^{\circ}}{12}=150^{\circ}\). The measure of an exterior angle \(E=\frac{360^{\circ}}{12}=30^{\circ}\).

Step4: For an 18 - gon

The sum of interior angles \(S=(18 - 2)\times180^{\circ}=16\times180^{\circ}=2880^{\circ}\). The measure of an interior angle \(A=\frac{(18 - 2)\times180^{\circ}}{18}=\frac{16\times180^{\circ}}{18}=160^{\circ}\). The measure of an exterior angle \(E=\frac{360^{\circ}}{18}=20^{\circ}\).

Answer:

15 - gon: An exterior angle measures \(24^{\circ}\)
16 - gon: The sum of the interior angles is \(2520^{\circ}\)
12 - gon: An interior angle measures \(150^{\circ}\)
18 - gon: An interior angle measures \(160^{\circ}\)