. If the measures of exterior angles of a pentagon is x o , 2x o , 3x o , 4x o , and 5x o , then find the largest exterior angle.
Question
If the measures of exterior angles of a pentagon is x°, 2x°, 3x°, 4x°, and 5x°, then find the largest exterior angle.
Solution
The sum of the exterior angles of any polygon is always 360 degrees.
Given that the exterior angles of the pentagon are x, 2x, 3x, 4x, and 5x, we can set up the equation:
x + 2x + 3x + 4x + 5x = 360
Adding the like terms gives:
15x = 360
To solve for x, divide both sides of the equation by 15:
x = 360 / 15
x = 24
The largest exterior angle is 5x, so substitute x = 24 into 5x:
5x = 5 * 24 = 120 degrees
So, the largest exterior angle of the pentagon is 120 degrees.
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