Question

The sum of three INTERIOR angles in a pentagon is 320° and the other two angles are(x+30)° and (x-70)°. Find x. *

Answer 1

We are told that we have a pentagon. That is, there are 5 interior angles and 5 sides. Recall that given a polygon of n sides, the sum of the interior angles is

`(n-2)\cdot180`

In a pentagon, we have n=5. So the sum of interior angles in this case would be

`(5\text{ -2)}\cdot180=3\cdot180=540`

Let us find the sum of the interior angles explicitly. We are told that two angles are (x+30) and (x-70). The other three angles sum up to 320. So the sum of the interior angles of this pentagon would be

`(x+30)+(x\text{ -70)+320}=2x+30+320\text{ - 70=2x+280}`

Now, we make this two quantities equal, so we have

`2x+280=540`

If we subtract 280 from both sides, we get

`2x=540\text{ -280=260}`

Now, we divide both sides by, so we get

`x=(260)/(2)=130`

So the value of x is 130