In a certain polygon, the exterior angle at each vertex measures 45 degrees. How

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Question: In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?

Options:

Correct Answer: 8

Solution:

The sum of the exterior angles of any polygon is 360 degrees. If each exterior angle is 45 degrees, the number of sides is 360 / 45 = 8.

In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?

In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?

Step 1: Understand that the sum of all exterior angles of any polygon is always 360 degrees.
Step 2: Know that in this polygon, each exterior angle measures 45 degrees.
Step 3: To find the number of sides, divide the total sum of the exterior angles (360 degrees) by the measure of each exterior angle (45 degrees).
Step 4: Perform the calculation: 360 divided by 45 equals 8.
Step 5: Conclude that the polygon has 8 sides.

Exterior Angles of a Polygon – The exterior angle at each vertex of a polygon is the angle formed between one side of the polygon and the extension of an adjacent side. The sum of all exterior angles of any polygon is always 360 degrees.
Calculating Number of Sides – To find the number of sides of a polygon when given the measure of each exterior angle, divide the total sum of exterior angles (360 degrees) by the measure of one exterior angle.