Question

Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°.​

Answer 1

$\dag\red{\widetilde{ \huge{ \underline{ \bf{ \color{hotpink}Solution: }}}}}$

▶Sum of the exterior angles of regular polygon =360°

▶Measures of each exterior angle =45°

Number of sides of regular polygon $\large{ \implies\bf{ \frac{ \red{360\degree}}{ \green{45 } {\degree} }}}$

$\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \color{blue} 8}$

∴ Polygon has 8 Sides.

Answer 2

Given that

• Exterior angle = 45°

Let number of sides = n

In a regular Polygon

Sum of the exterior angles = 360°

▶ Exterior Angle x Number of sides = 360°

➝ 45° x n = 360°

➝ n = 360°/ 45°

➡ n = 8

therefore polygon has 8 sides.

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