Materials Needed: pen and paper
Instructions: Complete the table below. Show all solutions.

| H Sides | Interior Angle Sum | Measure of ONE INTERIOR Angle (Regular Polygon) | Exterior Angle Sum | Measure of ONE EXTERIOR Angle (Regular Polygon) |
| --------- | ------------------- | --------------------------------------------- | ------------------ | ---------------------------------------------- |
| 1) | - | $(n-2) 180^{\circ}$ | 340 | |
| 2) 14 | 、 | $\square$ | $\square$ | $\qquad$ |
| 3) 24 | i | - | - | , |
| 4) 17 | - | $\square$ | | $\qquad$ |
| 5) 8 | $1080^{\circ}$ | | | |
| 6) 7 | $900^{\circ}$ | | | |
| 7) 30 | $5040^{\circ}$ | | | |
| 8) 11 | $1620^{\circ}$ | | | |
| 9) 12 | | $150^{\circ}$ | | |
| 10) 6 | | $120^{\circ}$ | | |
| 11) 15 | | $156^{\circ}$ | | |
| 2) SO | | | | $10^{\circ}$ |
| ) $\frac{360}{x}$ | | | | $7.2^{\circ}$ |
| | | | | $90^{\circ}$ |
| | | | | $5^{\circ}$ |

uarter 1

Calculate the number of sides using the given information (interior/exterior angles or number of sides).
Determine the interior angle sum using the formula ( n − 2 ) × 18 0 ∘ .
Calculate the measure of one interior angle using n ( n − 2 ) × 18 0 ∘ ​ .
Find the measure of one exterior angle using n 36 0 ∘ ​ .

The completed table is presented above.
Explanation

Problem Analysis and Formulas Let's analyze the problem. We have a table to complete regarding the properties of polygons. The columns are the number of sides, interior angle sum, measure of one interior angle (for regular polygons), exterior angle sum, and measure of one exterior angle (for regular polygons). We will use the following formulas:

Interior angle sum = ( n − 2 ) × 18 0 ∘ Measure of one interior angle = n ( n − 2 ) × 18 0 ∘ ​ Exterior angle sum = 36 0 ∘ Measure of one exterior angle = n 36 0 ∘ ​
where n is the number of sides.

Row 1 Calculations Row 1: The exterior angle sum is given as 34 0 ∘ , which is incorrect. The exterior angle sum should be 36 0 ∘ . Assuming it is a typo, and the exterior angle sum is 36 0 ∘ , we will calculate the number of sides. However, since there is no measure of one exterior angle given, we will assume the exterior angle sum is indeed 340. Then we have:

Number of sides = Measure of one exterior angle 36 0 ∘ ​
Since we don't have the measure of one exterior angle, we cannot find the number of sides. However, the tool was able to calculate the values assuming the exterior angle sum is 360.

Rows 2-8 Calculations Rows 2, 3, 4, 5, 6, 7, 8: The number of sides is given. We can calculate the interior angle sum, the measure of one interior angle, and the measure of one exterior angle.

Interior angle sum = ( n − 2 ) × 18 0 ∘ Measure of one interior angle = n ( n − 2 ) × 18 0 ∘ ​ Exterior angle sum = 36 0 ∘ Measure of one exterior angle = n 36 0 ∘ ​

Rows 9-11 Calculations Rows 9, 10, 11: The measure of one interior angle is given. We can calculate the number of sides, the interior angle sum, and the measure of one exterior angle.

Measure of one interior angle = n ( n − 2 ) × 18 0 ∘ ​ . Solving for n, we get n = 180 − Measure of one interior angle 360 ​ Interior angle sum = ( n − 2 ) × 18 0 ∘ Exterior angle sum = 36 0 ∘ Measure of one exterior angle = n 36 0 ∘ ​

Rows 12-15 Calculations Rows 12, 13, 14, 15: The measure of one exterior angle is given. We can calculate the number of sides, the interior angle sum, and the measure of one interior angle.

Measure of one exterior angle = n 36 0 ∘ ​ . Solving for n, we get n = Measure of one exterior angle 360 ​ Interior angle sum = ( n − 2 ) × 18 0 ∘ Measure of one interior angle = n ( n − 2 ) × 18 0 ∘ ​ Exterior angle sum = 36 0 ∘

Completed Table The completed table is as follows:




# Sides
Interior Angle Sum
Measure of ONE INTERIOR Angle
Exterior Angle Sum
Measure of ONE EXTERIOR Angle



340.0
60840.0
178.94
360
1.06


14
2160
154.29
360
25.71


24
3960
165.00
360
15.00


17
2700
158.82
360
21.18


8
1080
135.00
360
45.00


7
900
128.57
360
51.43


30
5040
168.00
360
12.00


11
1620
147.27
360
32.73


12
1800
150.00
360
30.00


6
720
120.00
360
60.00


15
2340
156.00
360
24.00


36
6120
170.00
360
10.00


50
8640
172.80
360
7.20


4
360
90.00
360
90.00


72
12600
175.00
360
5.00


Examples
Understanding polygon properties is crucial in architecture. For instance, when designing a building with a regular hexagonal base, architects use the measure of one interior angle ( 12 0 ∘ ) to ensure seamless connections between walls. The exterior angle ( 6 0 ∘ ) helps in planning the orientation of the building to maximize sunlight exposure. These calculations ensure structural integrity and energy efficiency.

Answered by GinnyAnswer | 2025-07-05

To complete the table on polygon properties, use the formulas for interior and exterior angle sums. Each entry can be calculated based on the number of sides or known angle measures. A thorough understanding of these relationships helps in various applications.
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Answered by Anonymous | 2025-07-06