SOLUTION: The new community swimming pool is pentagonal in a shape with three interior angles of 105 102 104 respectively. The other two interior angles have measures of 8x-11 and 4x. Find t

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Question 1036072: The new community swimming pool is pentagonal in a shape with three interior angles of 105 102 104 respectively. The other two interior angles have measures of 8x-11 and 4x. Find the measure of two missing angles
Answer by fractalier(6550) About Me  (Show Source):
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The number of degrees in a pentagon is found by 180(n-2) = 180(5-2) = 180(3) = 540 degrees. Since 311 degrees are spoken for in the three given angles, the two missing one must sum up to 540-311 = 229 degrees. Thus we write
8x - 11 + 4x = 229
12x - 11 = 229
12x = 240
x = 20
so that the two angles are
8(20) - 11 = 149 degrees and
4(20) = 80 degrees