Given
BC bisects ABD
∠ ABD =52°
prove: m ∠ABC=26°
To proof
As given in the question
BC bisects ∠ABD
This means BC divided ∠ABD into the two equal parts.
Therefore
[tex]\angle ABC = \frac{1}{2}\angle ABD[/tex]
As given
∠ABD = 52°
put this in the above value
we get
[tex]\angle ABC =\frac{1}{2}52^{\circ}[/tex]
∠ABC = 26°
Hence proved
An angle bisector divides the angle into equal halves.
Given that:
[tex]\angle ABD = 52^o[/tex]
From the question, we understand that:
BC bisects [tex]\angle ABD[/tex]
This means that:
[tex]\angle ABD = 2 \times \angle ABC[/tex] ---- By definition of midpoint
So, we have:
[tex]52^o= 2 \times \angle ABC[/tex] ---- By substitution property
Divide both sides by 2
[tex]26^o= \angle ABC[/tex] ---- By division property of equality
So, we have:
[tex]\angle ABC = 26^o[/tex] --- By symmetric property of equality
Hence,
[tex]\angle ABC = 26^o[/tex] --- proved
Read more about angle bisection at:
https://brainly.com/question/1921910
