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

Jayce Randolph

Mathematics

29 November, 06:19

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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Christian Long · 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