Jasmine is designing boxes she will use to ship her jewelry. She wants to shape the box like a regular polygon. In order for the boxes to pack tightly, she decides to use a regular polygon that has the property that the measure of its interior angles is half the measure of its exterior angles. What regular polygon should she use?

Question

Mathematics

Tramp

3 May, 01:46

Jasmine is designing boxes she will use to ship her jewelry. She wants to shape the box like a regular polygon. In order for the boxes to pack tightly, she decides to use a regular polygon that has the property that the measure of its interior angles is half the measure of its exterior angles. What regular polygon should she use?

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Answers (1)

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Yamilet · Answer 1

The regular polygon that she should use is an equilateral triangle

Step-by-step explanation:

The parameters given are;

Interior angles = 0.5 * Exterior angles

Exterior angles of a regular polygon = 360/n

Sum of interior angles of a regular polygon = (n - 2) * 180

Where n = the number of sides

Therefore, the sum of exterior angles of a regular polygon = 360°

Hence we have;

(n - 2) * 180 = 360/2 = 180

n - 2 = 180/180 = 1

n = 1 + 2 = 3 which is a three sided regular polygon or an equilateral triangle

Therefore, the regular polygon that she should use is an equilateral triangle