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°.

Step-by-step 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

$(14-2)\times 180^\circ\\\\=12\times 180^\circ\\\\=2160^\circ$

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°.