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

$m\angle EBD=\frac{m\angle CBD}{2}=\frac{42}{2}=21$

So,

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

m∠ABE=67°