Question

If the exterior angles of a convex octagon are x+13, 2x-1, 2x+6, 2x+12, 2x-17, 3x-4, 3x-10, and 4x calculate the smallest of the eight angles

Answer 1

The interior angles of an octagon add up to 360 degrees. Therefore the exterior angles, all add up to 1080 degrees. so add up all those expressions, then set them equal to 1080, then solve for x.

Answer 2

how do you do that

Answer 3

You already have 8 expressions that were given to you...just add them up....if you need help doing that, let me know.

Answer 4

i need help and thanks

Answer 5

you know how to add expressions, right? If you can add 2x + 4x, you can add those above...

Answer 6

Hmmm, I'm confident you know how to add them.....just add all the terms with x and all of the numerical terms

Answer 7

If you absolutely, positively can't figure it out, I'll show you the solution. But I would like for you to try.

Answer 8

i have no idea when i added i got 17x+7

Answer 9

Wait...I'll add them up...

Answer 10

Okay, I got an answer for x that gave a decimal...I'm going to verify my answer, then come back..

Answer 11

okay thanks!

Answer 12

Okay, so basically, when you add everything up you get 19x - 1 = 360

19x = 361

x = 19

The smallest angle is 2x - 17 so 2(19) - 17 = 21

There ya go!

Answer 13

thanks a lot!

Answer 14

thank you too! I got stumped with the second part and my teacher wasn't much help with explaining.