Question

1. Find the sum of the measures of the interior

angles of the indicated convex Polygon
B) 16-gon
A) 14-gon

Answer 1

A) Sum of angles in the 14-gon =
`2160^(o)`

B) Sum of angles in the 16-gon =
`2520^(o)`

Explanation:

Convex polygon is one that has the value of its internal angles less than the sum of angles in a triangle. That is each interior angle is less than
`180^(o)`.

Sum of angles in a polygon = (n - 2) x
`180^(o)`

where n is the value of its number of sides.

So that;

A) 14-gon (which has 14 sides),

Sum of angles in the 14-gon = (14 - 2) x
`180^(o)`

= 12 x
`180^(o)`

=
`2160^(o)`

The sum of the measure of the interior angles of the 14-gon is
`2160^(o)`.

B) 16-gon (which has 16 sides),

Sum of angles in the 16-gon = (16 - 2) x
`180^(o)`

= 14 x
`180^(o)`

=
`2520^(o)`

The sum of the measure of the interior angles of the 16-gon is
`2520^(o)`.