The angle bisector of <ABC is BP. If m<ABP is 86 degrees, what is m<ABC?

Answer 1

Hi Lexie,

The first best step to nearly all Geometry problems is to draw a picture.

Unfortunately, I can't draw in this box, so I'll have to be as descriptive as I can be.

The 3-point designation of the given angle ∠ABC indicates that point B is the Vertex.

So, draw an angle and mark the vertex point B. Where you mark points A and C isn't important, so long as they're on different sides of the angle.

AND DON'T WORRY ABOUT THE SCALE!

Next, we're told that segment BP is the angle bisector.

(Remember that a bisector cuts something exactly in half.)

There can only be ONE POINT labeled B in this problem, therefore we can add a segment that starts at the vertex B and connects to point P EXACTLY in the middle of the other two sides.

We can now see that ∠ABP is half of ∠ABC.

If m∠ABP = 86°, then m∠ABC = 172°. (Twice as much)

I hope this helps.