Answer: [tex]m\angle ABE=56\°[/tex]
Step-by-step explanation:
An Angle Bisector is defined as a line segment which divides an angle into two equal parts.
According to the information given in the exercise, you know that the angle bisector BE divides the angle ABC into two equal parts. These are:
[tex]m\angle ABE=2x+20\\\\m\angle EBC=4x-6[/tex]
Based on the definition given above, you know that:
[tex]m\angle ABE=m\angle EBC[/tex]
Then, you can write the following equation:
[tex]2x+20=4x-6[/tex]
Now you can solve for "x":
[tex]2x-4x=-20-6\\\\-2x=-26\\\\x=\frac{-26}{-2}\\\\x=13[/tex]
Finally, you must substitute the value of "x" into [tex]m\angle ABE=2x+20[/tex] and then evaluate:
[tex]m\angle ABE=2(13)+20\\\\m\angle ABE=26+20\\\\m\angle ABE=46\°[/tex]
