Question

worksheets
angles of polygons & similar triangles
total questions: 21
worksheet time: 1hrs 10mins

1. what is the sum of the angle measures in a nonagon (9 sides)?

a) 1440°
b) 900°
c) 1080°
d) 1260°

1. what is the sum of the angle measures in a hexagon (6 sides)?

a) 720°
b) 1080°
c) 600°
d) 540°

1. what is the sum of the angle measures in a triangle (3 sides)?

a) 60°
b) 90°
c) 120°
d) 180°

1. what is the measure of one interior angle in a regular pentagon (5-sides)?

a) 90°
b) 108°
c) 120°
d) 180°

1. what is the measure of one interior angle in a regular hexagon (6 sides)?

a) 60°
b) 80°
c) 108°
d) 120°

1. what is the measure of one interior angle in a regular triangle (3 sides)?

a) 15°
b) 30°
c) 60°
d) 90°

1. find the angle sum of the interior angles of the polygon.

a) 180°
b) 540°
c) 720°
d) 1080°

Explanation:

Step1: Recall polygon angle sum formula

The sum of interior angles of an $n$-sided polygon is $(n-2)\times180^\circ$. For regular polygons, one interior angle is $\frac{(n-2)\times180^\circ}{n}$.

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Question 1

Step1: Identify $n$ for nonagon

$n=9$

Step2: Calculate angle sum

$(9-2)\times180^\circ=7\times180^\circ=1260^\circ$

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Question 2

Step1: Identify $n$ for hexagon

$n=6$

Step2: Calculate angle sum

$(6-2)\times180^\circ=4\times180^\circ=720^\circ$

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Question 3

Step1: Identify $n$ for triangle

$n=3$

Step2: Calculate angle sum

$(3-2)\times180^\circ=1\times180^\circ=180^\circ$

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Question 4

Step1: Identify $n$ for pentagon

$n=5$

Step2: Calculate one interior angle

$\frac{(5-2)\times180^\circ}{5}=\frac{540^\circ}{5}=108^\circ$

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Question 5

Step1: Identify $n$ for hexagon

$n=6$

Step2: Calculate one interior angle

$\frac{(6-2)\times180^\circ}{6}=\frac{720^\circ}{6}=120^\circ$

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Question 6

Step1: Identify $n$ for triangle

$n=3$

Step2: Calculate one interior angle

$\frac{(3-2)\times180^\circ}{3}=\frac{180^\circ}{3}=60^\circ$

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Question 7

Step1: Identify $n$ for the polygon

The figure is a 5-sided polygon, $n=5$

Step2: Calculate angle sum

$(5-2)\times180^\circ=3\times180^\circ=540^\circ$

Answer:

1. d) $1260^\circ$
2. a) $720^\circ$
3. d) $180^\circ$
4. b) $108^\circ$
5. d) $120^\circ$
6. c) $60^\circ$
7. b) $540^\circ$