Question

The measures of 13 of the 14 angles of a 14−gon add up to 2,016°. What must the fourteenth angle measure be?

Answer 1

`x = 155 (1)/(13)` or 155 1/3 degrees. If you want a decimal, 155.076923 degrees.

Explanation:

2,016 is the sum of 13 identical numbers. Let's say the unknown number is
`x`. We'll now write an equation to solve it.

`13x = 2016`

Divide both sides by 13.

`x = (2016)/(13)`

Now, I went ahead and solved this and ended up with a repeating decimal. But for your sake we'll just make it a nice mixed number.

13 goes into 2016 155 times.

Here, I'll check for you.

`13 * 155 = 2015`

So, if we were to turn this into a mixed number, we'd get something like this.

`x = 155 (1)/(13)`

That should be your fourteenth angle measure.