Question

Solve for the unknown angle measures of the polygon. The measures of 13 of the 14 angles of a 14−gon add up to 2,040°. What must the fourteenth angle measure be?

Answer 1

Answer: The measure of fourteenth angle is 120°.

Explanation:

Since we have given that

Total number of angles in 14 gon = 14

Sum of measures of 13 angles = 2040°

As we know that sum of all angles in 14 gon would be

`(14-2)* 180^\circ\\\\=12* 180^\circ\\\\=2160^\circ`

So, the measure of fourteenth angle would be

`\sum_(x=1)^(13)+x_(14)=2160^\circ\\\\2040^\circ+x_(14)^\circ=2160^\circ\\\\x_(14)^\circ=2160-2040\\\\x_(14)^\circ=120^\circ`

Hence, the measure of fourteenth angle is 120°.