[tex]\angle ABC[/tex] can be congruent to [tex]\angle DBC[/tex] sometimes, if ray BC is an angle bisector of [tex]\angle ABC[/tex].
- In the diagram attached below shows two possible figures we can assume to get if ray BC is lies within [tex]\angle ABD[/tex].
- We are assuming that [tex]\angle ABD = 50^{\circ}[/tex]
- In figure 1, if ray BC lies within [tex]\angle ABD[/tex], we can have two angles that are not congruent to each other. We would have:
[tex]m \angle DBC = 30^{\circ}\\\\m \angle ABC = 20^{\circ}[/tex]
This implies that [tex]\angle ABC[/tex] will not always be congruent to [tex]\angle DBC[/tex] if ray BC lies within [tex]\angle ABD[/tex].
- In figure 1, if ray BC is an angle bisector and it lies within [tex]\angle ABD[/tex], we can have two angles that are congruent to each other. We would have:
[tex]m \angle DBC = 25^{\circ}\\\\m \angle ABC = 25^{\circ}[/tex]
This implies that [tex]\angle ABC[/tex] can sometimes be congruent to [tex]\angle DBC[/tex] if ray BC is an angle bisector that lies within [tex]\angle ABD[/tex].
- Therefore, we can conclude that:
[tex]\angle ABC[/tex] can be congruent to [tex]\angle DBC[/tex] sometimes, if ray BC is an angle bisector of [tex]\angle ABC[/tex].
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