SOLUTION: the measures of the interior angles of a convex pentagon ar 70 degrees, 87 degrees, 103 degrees, 2x degrees, and 3x degrees. what is the measure of the largest interior angles?

Algebra ->  Angles -> SOLUTION: the measures of the interior angles of a convex pentagon ar 70 degrees, 87 degrees, 103 degrees, 2x degrees, and 3x degrees. what is the measure of the largest interior angles?      Log On


   

Question 830176: the measures of the interior angles of a convex pentagon ar 70 degrees, 87 degrees, 103 degrees, 2x degrees, and 3x degrees. what is the measure of the largest interior angles?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
S = 180(n-2)

S = 180(5-2)

S = 180*3

S = 540

So all of the interior angles in a pentagon (regardless of what type of pentagon) add up to 540 degrees

So the angles 70 degrees, 87 degrees, 103 degrees, 2x degrees, and 3x degrees must add to 540

70 + 87 + 103 + 2x + 3x = 540

260 + 5x = 540

5x = 540-260

5x = 280

x = 280/5

x = 56

--------------------------------

2x = 2*56 = 112 degrees

3x = 3*56 = 168 degrees

--------------------------------

So the largest interior angle is 168 degrees