Question

2. Calculate the number of sides of a regular
polygon, if the measure of each interior
angle is 135 degree ​

Answer 1

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Given measure of each interior angle of polygon is 135°

To find the number of sides (n)=?

We know that each interior angle of a regualr convex n-gon has measure of

$\sf \frac{(n - 2) \times 180}{n}$

$\implies \sf \frac{n - 2 \times 180}{n} = 135 \\ \\ \implies \sf n - 2 \times 180 = 135n \\ \\ \sf \implies180n - 360 = 135n \\ \\ \implies \sf180n - 135 = 360 \\ \\ \implies \sf n = \frac{360}{45} = 8$

So the number of sides of polygpn is 8

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Answer 2

Answer:

The regular polygon has 8 sides. It is a regular octagon.

Step-by-step explanation:

Given,

Each interior angle of a polygon = 135°

To find, the number of sides of polygon(n) = ?

We know that,

Each interior angle of a regular convex n-gon has a measure of

$\frac{(n - 2) \times 180}{n} \\ \\ \frac{(n - 2) \times 180}{n} = 135 \\ \\ \implies(n - 2) \times 180 = 135n \\ \implies180n - 360 = 135n \\ \implies180n - 135n = 360 \\ \implies45n = 360 \\ \implies \: n = \frac{360}{45} = 8$

Hence, the regular polygon has 8 sides. It is a regular octagon.