Middle Grades Geometry Question Arithmetic Sequence

Question

Find the measures of each angle of a pentagon where the measures of the angles form an arithmetic sequence and the smallest measure is 60 deg.

Answer 1

The sum of the measures of the angles of a pentagon is (5-2)180 = 540

sum of arithmetic sequence

n(2a+ (n-1)d)/2

so given a is 60, n = 5, find d:

540 = 5(120+4d)/2

1080 = 600 + 20d

480 = 20d

d = 24

so sides are:

60, 84, 108, 132, 156