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disa [49]
3 years ago
5

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?
Mathematics
1 answer:
Jet001 [13]3 years ago
6 0

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°.

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