SOLUTION: The measures of the interior angles of a convex octagon are 45x, 40x, 155, 120, 155, 38x, 158, and 41x. What is the measure of the smallest interior angle?

Question 136001: The measures of the interior angles of a convex octagon are 45x, 40x, 155, 120, 155, 38x, 158, and 41x. What is the measure of the smallest interior angle?
Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
The sum of the interior angles of an octagon is 1080 degrees.
You were given:
45x, 40x, 155, 120, 155, 38x, 158, and 41x. You were told to find the smallest angle. The smallest angle is 38x but we need to find x first.
We add what has been given, equate to 1080 and solve for x.
45x + 40x + 155 + 120 + 155 + 38x + 158 + 41x = 1080

164x + 588 = 1080
Subtract 588 from 1080.
164x = 1080 - 588
164x = 492
Divide both sides by 164.
x = 492/164
x = 3
We now multiply 3 times 38 to find the smallest angle.
Smallest angle = 3 times 38
Smallest angle = 114
Is this clear?

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