Analyze which lines form the angles and find out what they are called. Then use the appropriate theorem or postulate to find the relationship between the angles.
Congruent, because vertical angles are congruent.
Practice makes perfect
Let's analyze the given diagram and find angles ∠ 3 and ∠ 6.
We are asked to find the relationship between these angles. To do that, we need to examine the lines these angles are formed by and the positions of the angles.
As we can see, ∠ 3 and ∠ 6 are two nonadjacent angles formed by two intersecting lines p and n. These are called vertical angles. To find the relationship between the angles, let's use the Vertical Angles Theorem.
Vertical Angles Theorem
If two angles are vertical angles, then they are congruent.
We conclude that angles ∠ 3 and ∠ 6 are congruent, which means that their measures are the same.
Extra
Example of Vertical Angles Seen in Everyday Life
Road signs are an everyday part of our lives. Beyond the signs we see and use in the States, streets worldwide use signs similar to those found in our neighborhoods. Here is an example of a road sign found in Japan that signifies a road closure. It can be read as tsuukoudome.
The following sign is another example of vertical angles being used. This road sign is seen in Vietnam.
It signifies that this area is not for stopping or parking. The translation comes from cấm dừng xe và đỗ xe. A very similar sign is found in Japan, which indicates the same meaning of no stopping or parking.
