Question

In the figure below, m LABD88°, m ZCBD42°, and BE bisects LCBD. Find mLABE.

Answer 1

We know

`m\angle ABD=88`

and are asked to find m∠ABE. One way we can do this is

`m\angle ABE=m\angle ABD-m\angle EBD`

Since

`m\angle CBD=42`

and BE bisects this angle, then

`m\angle EBD=(m\angle CBD)/(2)=(42)/(2)=21`

So,

`m\angle ABE=88-21=67,`

m∠ABE=67°