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gulaghasi [49]
3 years ago
12

=

Mathematics
1 answer:
svet-max [94.6K]3 years ago
8 0

Answer:

The polygon has 9 sides

Step-by-step explanation:

we know that

A regular polygon has equal length sides and equal interior angles

step 1

Find the measure of the interior angle

Remember that

The interior angle plus the exterior angle must be equal to 180 degrees (form a linear pair)

Let

x ----> the measure of each interior angle in the regular polygon

so

x+40^o=180^o

solve for x

x=180^o-40^o=140^o

step 2

Find the number of sides of the regular polygon

we know that

The measure of each interior angle in a regular polygon is given by the formula

x=\frac{(n-2)180^o}{n}

where

n is the number of sides of the polygon

substitute the given values

140^o=\frac{(n-2)180^o}{n}

solve for n

140n=180n-360\\180n-140n=360\\40n=360\\n=9\ sides

therefore

The polygon has 9 sides

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