Geometry prob: Find measure of angle 1 (pic included)?

Question

http://i1.tinypic.com/4xopcnd.jpg

i got:
x2 - 6x = x + 8
x2 = 7x + 8
x2 + 7x + 8 = 0

then i got confused
(by x2 i mean x squared)

you have to look at the pic, i need to find the MEASURE OF ANGLE 1. but thanks for clearing up half of it you guys!

Answer 1

What you have to do is to simply equate x2 - 6x = x+8 because they are vertical angles, and by vertical angle theorem, vertical angles are always congruent. So from
x2-6x=x+8, we arrive at: x2-7x-8=0.
By factoring methods, x2-7x-8=0 is similar with
(x+1)(x-8) = 0. to check with FOIL method, they are similar.
So, we equate x+1=0 and x-8=0 yielding x=-1 and x=8. Substituting, when x= -1, the two angles are 7 degrees
when x=8, the two angles are 16 degrees.
i hope its clear enough and have a good day!:D

Answer 2

First, your last line is incorrect as you'd have to subtract the x2 to set it all equal to zero, so it's -x2+7x+8=0, from there you have standard form for your problem, Ax2+Bx+C=0 then plug the variables into the quadratic formula found here, http://en.wikipedia.org/wiki/Quadratic_equation (it's the one where X= the square root of all the stuff over 2A) then solve for X.

Answer 3

I suppose that x^2=7x+8 is equal to x^2-7x-8=0
then, x=-1 or x=8
for x=-1 we get angle1='pi'-16 and for x=8 angle1='pi'-7

Answer 4

All righty..

Put the vertical angles equal to each other.
x2-6x=x+8

Then solve the algebra.

x2-7x-8=0
(x+1)(x-8)=0
x= -1,8

Answer 5

x^2-7x-8 = 0
(x-8)(x+7) = 0
x= 8 and x= -7

Answer 6

your third step should be x^2 -7x - 8

try reworking it