If C is in the interior of ∠ABD, thenm∠ABC + m∠CBD = m∠ABD
Angle Addition Postulate
Given that C is in the interior of ∠ABD, we can draw a diagram as shown below:
“`
A
/\
/ \
/ \
/∠ABC \
/ \
/__________\
B C D
∠CBD
“`
We know that the angle at B can be expressed as the sum of the two angles ∠ABC and ∠CBD, that is:
m∠ABD = m∠ABC + m∠CBD
This is due to the fact that the angle ∠ABD can be divided into two smaller angles ∠ABC and ∠CBD, as shown in the diagram above, and the sum of these two smaller angles will give us the angle at Vertex B, which is ∠ABD.
Thus, we can conclude that if C is in the interior of ∠ABD, then m∠ABC + m∠CBD = m∠ABD.
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