SOLUTION: In a convex octagon, three of the exterior angles each have a measure of xº. The other five exterior angles each have a measure of (2x+7)º. Find the measure of each exterior angl

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Question 963906: In a convex octagon, three of the exterior angles each have a measure of xº. The other five exterior angles each have a measure of (2x+7)º. Find the measure of each exterior angle.
Answer by macston(5194) About Me  (Show Source):
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The sum of the exterior angles of any polygon is 360 degrees, so:
(3)(x degrees) + (5)(2x+7 degrees) = 360 degrees
3x degrees + (10x+35) degrees=360 degrees Subtract 35 degrees from each side.
13x degrees=325 degrees Divide each side by 13.
x=25 degrees
The three smaller angles each measure 25 degrees.
The five larger angles measure (2x+7)=2(25)+7=57 degrees.
CHECK:
The sum of the exterior angles is 360 degrees.
3(25 degrees)+5(57 degrees)=360 degrees
75 degrees+285 degrees=360 degrees
360 degrees=360 degrees