algebra 2 help please?

Question

The degree measures of the angles of a pentagon are consecutive even integers. find the measure of the largest angle

step by step help please i need to understand this

Answer 1

penta (5) ....
(sides - 2) * 180 gives you total interior angle measure
(5-2) * 180 = 540

x
+(x+2)
+(x+4)
+(x+6)
+(x+8) ........ 5 consect.. EVEN angles .......... must add to 540

5x + 20 = 540
5x = 520
x = 104

104 + 106 + 108 + 110 + 112 = 540

Answer 2

Well first of all, realize that this is not a regular pentagon. Each angle is a different size.
Now, what you do know is that all the angles together must add up to be 540°. This is because just like all triangles add up to 180°, and all quadrilaterals to 360°, all pentagons add up to 540°.
After you see this, you must next take from the problem that the angle measures are consecutive. So...
x+x+1+x+2+x+3+x+4=540
Now simplify...
5x+10=540
Subtract 10 from both sides....
5x=530
And divide five from each side...
x=106.
BUT you're not done yet. 106° is the SMALLEST angle. To get the largest angle, you must add 4. (because they're consecutive.) So your final answer should be 110°.

Answer 3

Knowing that all 5 penatgon interior angles add up to 540 degrees (well, at least looking it up in wikipedia), and letting the largest angle =x, then each other angle must be x-2, x-4, etc degrees. So you have

x + (x -2) + (x-4) + (x-6) + (x-8) = 540 ==

5x - 20 = 540 ==

5x = 520 ==

x = 104 = the largest angle. Simple, huh?

Answer 4

S_Pentagon_angles = 3·pi/2=3·180º=540º

Angles: 2n-4, 2n-2, 2n, 2n+2, 2n+4 -->
10n=540º --> n=54º

--> The largest is 2·54º+4=112º

All angles: 104º, 106º, 108º, 110º, 112º

Saludos.