Analyze which lines form the angles. Determine their names and use the appropriate theorem or postulate.
Supplementary angles, see solution.
Practice makes perfect
To begin solving this exercise, let's draw the left part of the picture geometrically, using lines and arrows. To make the following explanations more clear to understand, let's give a name to each line.
To find the relationship between angles ∠ 3 and ∠ 4, we need to look at which lines form these two angles.
We can see that there is no name and, therefore, no theorem or postulate for the angles ∠ 3 and ∠ 4. So, let's use some other intermediate angle. For example, we can analyze ∠ 1 and ∠ 3.
We can see that ∠ 1 and ∠ 3 are corresponding angles. Therefore, we know that they are congruent angles. Because they are congruent angles, they have the same measure. Note that the measure of an angle can be written as m∠ 1. The m for that writing is not the same as the name of the line in the diagram.
m∠ 1=m∠ 3
Also, the diagram shows us that ∠ 1 and ∠ 4 form a linear pair, which indicates to us that they are supplementary angles.
m∠ 1+ m∠ 4=180^(∘)
By substituting m∠ 1 with m∠ 3 in the above equality, we get the following.
m∠ 3+ m∠ 4=180^(∘)
Therefore, angles ∠ 3 and ∠ 4 are also supplementary angles.
