Question

In the following diagram, BD is the angle bisector of m

Answer 1

141°

Explanation:

If BD is an angle ABC bisector, then by angle bisector definition,

`m\angle ABD=m\angle DBC`

Given

`m\angle ABD=10x-17\\ \\m\angle DBC=6x+18`

Therefore,

`10x-17=6x+18\\ \\10x-6x=18+17\\ \\4x=35\\ \\x=(35)/(4)=8.75`

Now, find the measure of the whole angle ABC:

`m\angle ABC=2m\angle ABD=2(10x-17)^(\circ)=(20x-34)^(\circ)=\\ \\=(20\cdot 8.75-34)^(\circ)=141^(\circ)`