In this exercise we are asked to use the given figure to determine the relationship between ∠ ABD and ∠ BDA. Let's consider the given diagram. We will mark the angles we are interested in.
If one side of a triangle is longer than another side, then the angle opposite the longer side has greater measure than the angle opposite the shorter side.
From the diagram, we can see that ∠ ABD is opposite to side AD and ∠ BDA is opposite to side AB. Note that we are given the measurements for these segment lengths. Let's compare them.
AD&=13
AB&=3
We know that AD is longer than AB. Therefore, from the theorem about the Angle-Side Relationships in Triangles we can conclude that m∠ ABD is greater than m∠ BDA.
