Analyze which lines form the angles. Determine their names and use a corresponding theorem or postulate to figure out what their relationship is.
Supplementary angles, see solution.
Practice makes perfect
Let's start by drawing a visual of the left part of the picture geometrically using lines and arrows. We can also name the lines to make the following explanations to be more clear to follow and understand.
We are asked to find the relationship between angles ∠ 1 and ∠ 2. Take a look at the diagram to determine which lines form these two angles.
The use of supplementary angles in the real world is very common. Consider cutting a single piece of straight-angled wood to make a picture frame.
Once this piece is cut by the transversal, two pieces of wood are created that can be put together. They can fit perfectly together by rotating and flipping it to match the supplementary angle of the left piece.
Thanks to supplementary angles, the same process can be followed to complete the frame. Take a look at any picture frame and think about how the corners were cut and pieced together!
