Question

interior angle
find the interior angle of each regular polygon. round your answer to the nearest tenth.
1)
sum of the interior angles = ____
each interior angle = ____
2)
sum of the interior angles = ____
each interior angle = ____
3)
sum of the interior angles = ____
each interior angle = ____
4)
sum of the interior angles = ____
each interior angle = ____
5)
sum of the interior angles = ____
each interior angle = ____
6)
sum of the interior angles = ____
each interior angle = ____
7)
sum of the interior angles = ____
each interior angle = ____
8)
sum of the interior angles = ____
9)
sum of the interior angles = ____
each interior angle = ____

find the interior angle of each regular polygon. round your answer to the nearest tenth.
1)
sum of the interior angles = ____
each interior angle = ____
2)
sum of the interior angles = ____
each interior angle = ____
3)
sum of the interior angles = ____
each interior angle = ____
4)
sum of the interior angles = ____
each interior angle = ____

1. regular 11-gon

sum of the interior angles = ____
each interior angle = ____

1. regular 13-gon

sum of the interior angles = ____
each interior angle = ____

1. regular 17-gon

sum of the interior angles = ____
each interior angle = ____

1. regular 14-gon

sum of the interior angles = ____

Explanation:

Step1: Recall polygon angle formulas

Sum of interior angles: $(n-2) \times 180^\circ$, where $n$ = number of sides. Each interior angle (regular polygon): $\frac{(n-2) \times 180^\circ}{n}$

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Top Worksheet (1-9)

Step2: Solve 1) Octagon ($n=8$)

Sum: $(8-2) \times 180 = 6 \times 180 = 1080^\circ$
Each angle: $\frac{1080}{8} = 135.0^\circ$

Step3: Solve 2) Square ($n=4$)

Sum: $(4-2) \times 180 = 2 \times 180 = 360^\circ$
Each angle: $\frac{360}{4} = 90.0^\circ$

Step4: Solve 3) Decagon ($n=10$)

Sum: $(10-2) \times 180 = 8 \times 180 = 1440^\circ$
Each angle: $\frac{1440}{10} = 144.0^\circ$

Step5: Solve 4) Pentagon ($n=5$)

Sum: $(5-2) \times 180 = 3 \times 180 = 540^\circ$
Each angle: $\frac{540}{5} = 108.0^\circ$

Step6: Solve 5) Nonagon ($n=9$)

Sum: $(9-2) \times 180 = 7 \times 180 = 1260^\circ$
Each angle: $\frac{1260}{9} = 140.0^\circ$

Step7: Solve 6) Hexagon ($n=6$)

Sum: $(6-2) \times 180 = 4 \times 180 = 720^\circ$
Each angle: $\frac{720}{6} = 120.0^\circ$

Step8: Solve 7) Heptagon ($n=7$)

Sum: $(7-2) \times 180 = 5 \times 180 = 900^\circ$
Each angle: $\frac{900}{7} \approx 128.6^\circ$

Step9: Solve 8) Triangle ($n=3$)

Sum: $(3-2) \times 180 = 1 \times 180 = 180^\circ$
Each angle: $\frac{180}{3} = 60.0^\circ$

Step10: Solve 9) Heptagon ($n=7$)

Sum: $(7-2) \times 180 = 5 \times 180 = 900^\circ$
Each angle: $\frac{900}{7} \approx 128.6^\circ$

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Bottom Worksheet (1-8)

Step11: Solve 1) Octagon ($n=8$)

Sum: $(8-2) \times 180 = 6 \times 180 = 1080^\circ$
Each angle: $\frac{1080}{8} = 135.0^\circ$

Step12: Solve 2) 11-gon ($n=11$)

Sum: $(11-2) \times 180 = 9 \times 180 = 1620^\circ$
Each angle: $\frac{1620}{11} \approx 147.3^\circ$

Step13: Solve 3) Square ($n=4$)

Sum: $(4-2) \times 180 = 2 \times 180 = 360^\circ$
Each angle: $\frac{360}{4} = 90.0^\circ$

Step14: Solve 4) 10-gon ($n=10$)

Sum: $(10-2) \times 180 = 8 \times 180 = 1440^\circ$
Each angle: $\frac{1440}{10} = 144.0^\circ$

Step15: Solve 5) 11-gon ($n=11$)

Sum: $(11-2) \times 180 = 9 \times 180 = 1620^\circ$
Each angle: $\frac{1620}{11} \approx 147.3^\circ$

Step16: Solve 6) 13-gon ($n=13$)

Sum: $(13-2) \times 180 = 11 \times 180 = 1980^\circ$
Each angle: $\frac{1980}{13} \approx 152.3^\circ$

Step17: Solve 7) 17-gon ($n=17$)

Sum: $(17-2) \times 180 = 15 \times 180 = 2700^\circ$
Each angle: $\frac{2700}{17} \approx 158.8^\circ$

Step18: Solve 8) 14-gon ($n=14$)

Sum: $(14-2) \times 180 = 12 \times 180 = 2160^\circ$
Each angle: $\frac{2160}{14} \approx 154.3^\circ$

Answer:

Top Worksheet

1. Sum of interior angles = $1080^\circ$, Each interior angle = $135.0^\circ$
2. Sum of interior angles = $360^\circ$, Each interior angle = $90.0^\circ$
3. Sum of interior angles = $1440^\circ$, Each interior angle = $144.0^\circ$
4. Sum of interior angles = $540^\circ$, Each interior angle = $108.0^\circ$
5. Sum of interior angles = $1260^\circ$, Each interior angle = $140.0^\circ$
6. Sum of interior angles = $720^\circ$, Each interior angle = $120.0^\circ$
7. Sum of interior angles = $900^\circ$, Each interior angle = $128.6^\circ$
8. Sum of interior angles = $180^\circ$, Each interior angle = $60.0^\circ$
9. Sum of interior angles = $900^\circ$, Each interior angle = $128.6^\circ$

Bottom Worksheet

1. Sum of interior angles = $1080^\circ$, Each interior angle = $135.0^\circ$
2. Sum of interior angles = $1620^\circ$, Each interior angle = $147.3^\circ$
3. Sum of interior angles = $360^\circ$, Each interior angle = $90.0^\circ$
4. Sum of interior angles = $1440^\circ$, Each interior angle = $144.0^\circ$
5. Sum of interior angles = $1620^\circ$, Each interior angle = $147.3^\circ$
6. Sum of interior angles = $1980^\circ$, Each interior angle = $152.3^\circ$
7. Sum of interior angles = $2700^\circ$, Each interior angle = $158.8^\circ$
8. Sum of interior angles = $2160^\circ$, Each interior angle = $154.3^\circ$