Analyze which lines form the angles. Find out their names and use a corresponding theorem or postulate.
Congruent angles, see solution.
Practice makes perfect
We know that a solar dish collects energy by directing radiation from the Sun to a receiver located at the focal point of the dish. We will determine the relationship between the angles ∠ 4 and ∠ 5 formed by the radiation rays. We can start by drawing the left part of the picture geometrically using lines and arrows. Let's name the lines so the following explanations will be easier.
In order to find the relationship between angles ∠ 4 and ∠ 5, we can look at which lines form these two angles. It helps to highlight the findings.
Analyzing the diagram, we see that ∠ 4 and ∠ 5 are exterior angles of the parallel lines l and k. Now that we have identified them, let's note their characteristics. It appears that they lie on opposite sides of the transversal e. These are called alternate exterior angles. Therefore, we can use the Alternate Exterior Angles Theorem.
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.
Using the theorem, we conclude that ∠ 4 and ∠ 5 are congruent angles, or angles of the same measure.
