Question

part 1: finding the sum of interior a
a polygon is a closed plane figure made up of____or more line segments that intersect
at their end points.
the sum s of the interior angle measures of polygon with n sides is:

find the sum of the interior angle
measures of the school crossing sign.
the sign is in the shape of a pentagon.
it has 5 sides.

find the sum of the interior angle measures of the green polygon.
a)

number of sides =____
sum of interior angles =____
b)

number of sides =____
sum of interior angles =____
for polygons whose names you have not learned, you can use the phrase

• gon,\ where n is the number of

sides. for example, a 15 - gon is a polygon with 15 sides.
c)
12 - gon
number of sides =____
sum of interior angles =____
d)
17 - gon
number of sides =____
sum of interior angles =____

Explanation:

Step1: Count sides for a)

The green polygon in a) is a square (4 - sided).

Step2: Calculate sum for a)

Using \(S=(n - 2)\cdot180^{\circ}\), substitute \(n = 4\).
\(S=(4 - 2)\cdot180^{\circ}=2\cdot180^{\circ}=360^{\circ}\)

Step3: Count sides for b)

The green polygon in b) is a hexagon (6 - sided).

Step4: Calculate sum for b)

Using \(S=(n - 2)\cdot180^{\circ}\), substitute \(n = 6\).
\(S=(6 - 2)\cdot180^{\circ}=4\cdot180^{\circ}=720^{\circ}\)

Step5: Interpret 12 - gon for c)

A 12 - gon has \(n = 12\) sides.

Step6: Calculate sum for c)

Using \(S=(n - 2)\cdot180^{\circ}\), substitute \(n = 12\).
\(S=(12 - 2)\cdot180^{\circ}=10\cdot180^{\circ}=1800^{\circ}\)

Step7: Interpret 17 - gon for d)

A 17 - gon has \(n = 17\) sides.

Step8: Calculate sum for d)

Using \(S=(n - 2)\cdot180^{\circ}\), substitute \(n = 17\).
\(S=(17 - 2)\cdot180^{\circ}=15\cdot180^{\circ}=2700^{\circ}\)

Answer:

a) Number of Sides \(=4\), Sum of interior angles \(=360^{\circ}\)
b) Number of Sides \(=6\), Sum of interior angles \(=720^{\circ}\)
c) Number of Sides \(=12\), Sum of interior angles \(=1800^{\circ}\)
d) Number of Sides \(=17\), Sum of interior angles \(=2700^{\circ}\)