Answer:
x = 11
Explanation:
Assuming that segment EG is a diameter we can solve this using the straight angle theorem ( Which states that angles on a straight line add up to equal 180. Also note that central angles and there corresponding arcs are congruent. )
We are also told that CH is a bisector.
A bisector splits an angle into TWO EQUAL parts.
mDG is split into mDC and mCG
So mDC = mCG
This meaning that because mDC = 7x + -1 , mCG also equals 7x - 1
Leading to us having enough information to use the straight line theorem ( which also works with half circles and arcs. )
So 180 = 2 ( 7x - 1 ) + 2x + 6
now we solve for x
step 1 distribute the 2
2 * 7x = 14x
2 * - 1 = -2
now we have 180 = 14x - 2+ 2x + 6
step 2 combine like terms
14x + 2x = 16x
-2 + 6 = 4
now we have 180 = 16x + 4
step 3 subtract 4 from each side
4 - 4 cancels out
180 - 4 = 176
Now we have 176 = 14x
step 4 divide each side by 14
176 / 16 = 11
14x/14 = x
we're left with x = 11