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In a certain polygon, the exterior angle at each vertex measures 45 degrees. How
In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?
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In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?
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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.
Questions & Step-by-step Solutions
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Q
Q: In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?
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.
Steps: 5
Show Steps
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.
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