Question

How many sides does a regular polygon have if the measure of each external angle is 45°?

Answer 1

Answer:

Sum of exterior angle of any polygon is 360° . As each exterior angle is 45°, number of angles or sides of the polygon is 360°×45°=8 .

A regular octagon has eight equal sides and eight equal angles.

(a) Calculate the size of each exterior angle in the regular octagon. We do this by dividing 360° by the number of sides, which is 8. The answer is 360° ÷ 8 = 45°.

A regular polygon with an exterior angle measure of 40 degrees has nine sides. Every polygon's exterior angle sum equals 360. So 360/40 equals nine.

It works by constructing an isosceles right triangle, which has interior angles of 45, 45 and 90 degrees. We use one of those 45 degree angles to get the result we need.

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