Unit 6 Regular Polygons

The measure of the smallest interior angle of the heptagon is 125.7°.

Step-by-step Explanation:

1. Understanding the problem:

– We have a heptagon (7-sided polygon) where each interior angle differs from the next by 25°.

– We need to find the measure of the smallest interior angle of this heptagon to the nearest tenth of a degree.

2. Formula for the interior angles of a polygon:

The formula to find each interior angle of a regular n-sided polygon is:

Interior angle = $\frac{(n-2) \cdot 180^{\circ}}{n}$

For a heptagon (n = 7):

Interior angle = $\frac{(7-2) \cdot 180^{\circ}}{7}=\frac{5 \cdot 180^{\circ}}{7}=128.5714^{\circ}$

3. Understanding the sequence of angles:

– The problem states that each interior angle is put in increasing order, each differing from the next by 25°.

– Therefore, the angles are:

128.5714°, 153.5714°, 178.5714°, 203.5714°, 228.5714°, 253.5714°, 278.5714°

4. Finding the smallest angle:

– The smallest angle in this sequence is 128.5714°.

5. Rounding to the nearest tenth:

– Rounding 128.5714° to the nearest tenth gives 125.7°.

Therefore, the measure of the smallest interior angle of the heptagon is 125.7° to the nearest tenth of a degree.

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