Given that 𝐴𝐵 is parallel to 𝐶𝐷, find the measure of angle 𝐸𝐹𝐵.
First of all, just to clarify some of the notation within the question, in particular this piece here, the double forward slash. Now as I read the question, you’ve heard me say 𝐴𝐵 is parallel to 𝐶𝐷. So that is what is meant by this notation. So we can include the information on our diagram by adding this pair of arrows that I’ve added in blue.
So let’s clarify which angle we’re looking for. We’re asked for angle 𝐸𝐹𝐵, so that means the angle formed when I travel from 𝐴 to 𝐹 to 𝐵. So it’s this angle that I have marked in orange in the diagram. Now looking carefully at the diagram, we know we have this pair of parallel lines and then we have a line cutting through them, a line that’s known as a transversal. So in order to answer this question, we’ll be using our angle rules about angles in parallel lines. We’ve also been given an angle of 52 degrees that we’d need to use within our answer.
So let’s think back to the different types of angles that we know about in parallel lines and transversals. We have three main types: corresponding angles, co-interior angles, and alternate angles. We can determine whether the angle of 52 degrees and the angle we’re looking for are any of these types of angles by looking at their position. In a simplified version of the diagram, we can see that these two angles are actually corresponding angles because they’re in the same position on the two parallel lines. They’re both the angles to the right of the transversal and above the parallel lines, which means they’re corresponding.
So now we’ve identified the type of angles we have, we need to remember the angle rule about them. And the key fact about corresponding angles is that they’re equal. So this gives us all the information we need in order to calculate angle 𝐸𝐹𝐵. As angle 𝐸𝐹𝐵 is corresponding to the angle of 52 degrees, it must be equal to 52 degrees. So we have our answer to the problem. 𝐸𝐹𝐵 is equal to 52 degrees.
Now, looking at the diagram, we can have some confidence in our answer because the angle we were asked to find is an acute angle. So 52 degrees is certainly the right type of value for this angle. So within this question about angles in parallel lines, we looked at the positioning of the angle we knew and the angle we wanted to find. And from the positioning of those two angles, we were able to recognize that they’re corresponding angles. And then using the fact that corresponding angles are equal gave us our answer to the problem.