ACT 13: Finding a Missing Angle from Parallel Lines Cut By a Transversal

Added: 2026-05-22

[00:00:01]Hello and welcome. So we have this particular  question which we're told that lines x and y are parallel. They're cut by transversals c and  w. All right. And we're given that angle B is 12 degrees. So that means that up here, right,  this angle is 12 degrees. Um, I'm gonna do this it's a little bit better, not by much. So 12  degrees. All right. We're told that angle N is 64 degrees. So that means 64 is down here. And  we're asked to find the measure of angle F. F is right down here, alrighty. So in order to do  that there's a couple of pieces of information we need to know but not a lot. We actually don't  even need to know that N is 64 in order to solve this problem. Now where we can go from here is  you could say all right, well we know there are four congruent angle theorems when it comes  to parallel lines and transversals. The first one is what we call vertical angles. If you have  angles that are directly vertical of each other they have to be congruent. So that means B and C,  they are vertical angles. They must be congruent, the same. They're both 12 degrees. Okay. We have  another angle theorem that says that you have um alternate interior angles. So angle C and angle  G would be an example of alternate interior angles because they are both inside of the parallel  lines on the alternate side of the transversal.

[00:01:38]Okay, which means that's also 12. Another way  we could do this is that from C you could also notice that H is congruent. This is what we  call a corresponding angle. Now you'll notice that this is like the bottom left angle  at C. Well it's the bottom left angle at H so that would make them congruent to  each other. So this would also be 12 degrees.

[00:02:02]Okay. The only one left is an alternate exterior  angle which ironically we also have as well.

[00:02:07]An alternate exterior angle pair would be  like example B and H where they're outside on the exterior of your parallel lines and  then they are on the alternate side of the transversal. So those are your four congruent  angle theorems. Now from there how do we find angle F? Because clearly F and G or F and H  are not the same. Well we can use one last idea, where we know that half of a line has to  be 180 degrees. You're like wow Miss Ditty, how do we know that? Well the reason why we do is if  you think about a circle. If you have a diameter of a circle that cuts your circle in half, a  circle all the way around is 360 degrees, which means that if you're cutting it in half only  halfway around the circle would be, whoops, 180 degrees. And that's how we know that our  angle H and F add up to 180. You could also do angle F and G add up to 180 because they're 12 in both cases it will not matter how you set it up as long as they're on the  same side of a line. So that means that you do 180 take away the 12 and we're left with  168. And that will be, the angle of measure F.

[00:03:30]I said that backwards. The measure of angle F.  We also know that 168 is one of the choices down below. There you go. There's your  answer. Alrighty, thanks for watching.