Question

I NEED ANSWER REALLY FAST IN GEOMETRY 40 POINTS

The diagram shows a certain construction technique. If
mABF = x + 10x - 1, mCBF = 12x + 7,
what is mLCBF?

Answer 1

m∠CBF = 55°

If f bisects angle ABC, then mABF and mCBF should be equal to one another. This means we can set up an equation:
x + 10x -1 = 12x +7

Now evaluate for x, and we get
x = -2, x = 4. Plugging in each value to the original equation, we find it cannot be -2 since angles are positive values. This leaves x = 4.
mCBF = 12(4) + 7 = 55.

Here is a photo of my work, it is hard to type it out on my phone: