Question

Find the number or sides of a regular polygon if each of its interior angles measures: 140°​

Answer 1

Answer:

What is the name of a polygon whose interior angles are each 140°? Subtract both sides by 180°n. = 9. Therefore, the number of sides is 9

Step-by-step explanation:

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Answer 2

Let the sides of a regular polygon be n.

Sum of interior angles of a n sided polygon

$= (2n - 4) \times 90$

For a regular polygon each interior angle

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

As given,

Each interior angle = 140

Therefore,

$140 = \frac{(2n - 4) \times 90}{n}$

$140n= (2n - 4) \times 90$

$140n = 180n - 360$

$180n - 140n = 360$

$40n = 360$

$n = \frac{360}{40} = 9$

No. of sides of a regular polygon = 9