Question

This is a polygon and I need help finding the missing angle ?

Answer 1

First, you need to know that the total (degrees) of the interior angles is 360 because this is a quadrilateral.

The unnumbered angle is 109 degrees. We know this because the angle labeled 71 degrees and the unnumbered angle are supplementary. So you subtract 180 from 71 to get 109. 
$180-71=109$

To solve for x, we need to realize the other numbers playing into the angles' values. To make solving this easier, I'm gonna assign letters to the angles. 

(10x+6) is angle A. 

(13x-2) is angle B. 

(8x-1) is angle C.

and 109 (the one we solved) is angle D. 

We know that the total of the interior angles is 360, so we can add the 2 from angle B and the 1 from angle C to 360. This is because these numbers are subtracted from the other values. 
$360+2+1=363$

Now, we have to subtract the 6 from angle A from 363, because the 6 is added to the other values. 
$363-6=357$

Now we have to subtract 109 from 357 because you want to get the x's by themselves. Since you're solving for x. 
$357-109=248$

That leaves you with 248. Now you add all the x's up to get the total number of x's. You have 10x from angle A, 13x from angle B, and 8x from angle C. 
$10x+13x+8x=31x$

You get 31x. To get what x is, you divide 248 by 31. 
$\frac{248}{31} =8$

That equals 8. So now that you know that x equals 8, if you need to find the values of the angles, you just plug in the numbers into the formulas. 

$(10(8))+6= 86$
$(13(8))-2=102$
$(8(8))-1=63$
$109$

Check your work by plugging your answers in and seeing if they add up to 360. 
$86+102+63+109=360$

Which they should:)

So...
angle A= 86
angle B=102
angle C=63
angle D=109

and x=8



Hope this helped!!!