BX is the Angle Bisector of < ABC

Question

BX is the Angle Bisector of < ABC

Answer 1

So this question is testing on if you know what the definition of an angle bisector is, and it's characteristics. It splits the larger angle ABC in half.

1. You are given the large angle ABC = 4X + 16
2. You are given 1/2 of the larger angle with the smaller angle CBX = 3X + 6
3. So you could multiply the smaller angle equation by 2 and this would equal the larger angle, so
4. 4X + 16 = 2(3X + 6); now you can solve for X
5. 4X + 16 = 6X + 12; gather like terms then isolate the X
6. 4 = 2X
7. X = 2

I hope this helped you to understand it; does this make sense to you?