Question

angles of a certain polygon are in arithmetic sequence. The smallest interior angle measures 80 degrees and the largest interior angle measures 160 degrees. How many sides does the polygon have?
Plz show me work i don't know it at all plz

Answer 1

sum of n terms of an AP if you know the first and last is
sum = (first + last)(n/2)
sum = (80+160)(n/2) = 120n
but we know that the sum of the interior angles of a polygon = 180(n-2)

so 120n = 180n - 360
-60n=-360
n = 6

your figure is an irregular hexagon

check: sum of angles in a hexagon = 180(6-2) = 720
our angles ....
a = 80
angle 6 = term(6) = a+5d = 160
80+5d=160
5d=80
d = 16

the angles are: 80, 96, 112, 128, 144, 160
add them up to show their sum = 720, it is.

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