In this exercise we want to find the measure of angle ∠ ABC. First, consider the given diagram.
Note that angle ∠ ABC is an angle divided into two smaller angles, ∠ ABD and ∠ DBC. These two angles are adjacent angles. Since we know their measures, we can use the Angle Addition Postulate to find the measure of ∠ ABC. Let's recall what this postulate states.
Angle Addition Postulate
If P is in the interior of ∠ RST, then the measure of ∠ RST is equal to the sum of the measures of ∠ RSP and ∠ PST.
This tells us that we can find the measure of an angle by adding the measures of the smaller adjacent angles contained by the larger one. Translating this into terms of our exercise, we get that the measure of ∠ ABC is the sum of measures of angles ∠ ABD and ∠ DBC. We can write this using symbols.
m∠ ABC = m∠ ABD+ m∠ DBC
Finally, since we know that m∠ ABD= 37^(∘), and m∠ DBC= 21^(∘), we can substitute these values into the above equation.
m∠ ABC= 37^(∘)+ 21^(∘)=58^(∘)
The measure of ∠ ABC is 58^(∘).
