Question

find the number of sides of a regular polygon if it's each interior angle is 135°

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Answer 1

⍟ Solution ⍟

Given :-

• The polygon is regular

• It's each interior angle is 135°

To-find :-

• Number of sides of given polygon

Formula :-

$\frac{(2n - 4) \times 90^{\circ}}{n}$

Now , we should substitute the given values in this formula to find the sides of the polygon

⇛$135 = \frac{(2n - 4) \times 90^{\circ}}{n}$

⇛$135n = 180n - 360^{\circ}$

⇛$180n - 135n = 360^{\circ}$

⇛$45n = 360^{\circ}$

⇛$n = \frac{360^{\circ}}{45}$

⇛$n = 8$

Therefore , the given polygon is madeup of 8 sides and the polygon with 8 sides is known as " octagon "