Question

How many sides does a regular polygon have if each interior angle measures 176^{\circ}
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Answer 1

It's equilateral polygon

• Sum of interior angles=176n.

n is no of sides

`\\ \sf\longmapsto (2n-4)90=176n`

`\\ \sf\longmapsto 180n-360=176n`

`\\ \sf\longmapsto 180n-176n=360`

`\\ \sf\longmapsto 4n=360`

`\\ \sf\longmapsto n=4`

Answer 2

• 90 sides

Explanation:

There is a relationship between number of sides and interior angle measure of regular polygons:

• S = 180(n - 2), where S- sum of interior angles, n - number of sides

We have now:

• 176n = 180(n - 2)
• 176n = 180n - 360
• 4n = 360
• n = 90