Question

Help me and i’ll mark you brainliest plus you get 20 points !!!!

Answer 1

Answer:

Angle bisector

Step-by-step explanation:

Find the measure of the angle COA. By angle addition postulate,

$m\angle COX=m\angle AOX+m\angle COA$

From the diagram,

$m\angle COX=80^{\circ}\\ \\m\angle AOX=40^{\circ},$

then

$80^{\circ}=m\angle COA+40^{\circ}\\ \\m\angle COA=80^{\circ}-40^{\circ}=40^{\circ}$

Find the measure of the angle BOA. By angle addition postulate,

$m\angle BOX=m\angle AOX+m\angle BOA$

From the diagram,

$m\angle BOX=60^{\circ}\\ \\m\angle AOX=40^{\circ},$

then

$60^{\circ}=m\angle BOA+40^{\circ}\\ \\m\angle BOA=60^{\circ}-40^{\circ}=20^{\circ}$

Find the measure of the angle COB. By angle addition postulate,

$m\angle COX=m\angle BOX+m\angle COB$

From the diagram,

$m\angle BOX=60^{\circ}\\ \\m\angle COX=80^{\circ},$

then

$80^{\circ}=m\angle COB+60^{\circ}\\ \\m\angle COB=80^{\circ}-60^{\circ}=20^{\circ}$

This means, the measures of angles COB and BOA are the same and are equal half the measure of angle COA, so angles COB and BOA are congruent. This means, the ray OB is the angle bisector of angle COA