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

Answer:

$x = 155 \frac{1}{13}$ or 155 1/3 degrees. If you want a decimal, 155.076923 degrees.

Step-by-step 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.

$x = \frac{2016}{13}$

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.

$x = 155 \frac{1}{13}$

That should be your fourteenth angle measure.