Question

the degree measures of the interior angles of a concave hexagon from an arithmetic sequence. the smallest angle measures 35 degrees. how many degrees are there in the measure of the largest angle?

Answer 1

205°

Explanation:

an hexagon has 6 sides.

Sum of angles in a polygon = (2n-4) * 90

for hexagon, =(2*6 - 4) *90 = 720°

Since the angles of the hexagon forms an arithmetic sequence,the angles will be;

a,a+d, a+2d, a+3d,a+4d,a+5d

a+a+d+a+2d+a+3d+a+4d+a+5d =720

6a+15d =720

15d = 720 -6a

but a= 35 degrees

15d = 720 -(6*35)

15d =510

d=34°

the largest angle is a+5d = 35 + (5*34)

= 205°