In the figure, use the information given to determine the measure of angle 𝐴𝐶𝐷.
Now in these types of questions, the first thing I do is actually mark on any angles I actually know or I can calculate. And I would start with angle 𝐵𝐴𝐶. And I can say that angle 𝐵𝐴𝐶 is gonna be equal to 180 minus 88 which is 92 degrees. But in these questions, what I always say you must remember to do is not just calculate the angle but also give your reasoning. And our reasoning for this is that it is 92 degrees as angles on a straight line are equal to 180 degrees.
Okay, so fantastic, we’ve worked out the first thing that we can which is angle 𝐵𝐴𝐶. Well, the next angle we can move on to is angle 𝐵𝐴𝐸. And we can see that angle 𝐵𝐴𝐸 is gonna be equal to 180 minus 145 which is equal to 35 degrees. And again, we’ve got to give our reasoning for this. And our reasoning is, in fact, the same as the first angle which was angle 𝐵𝐴𝐶. And that is it’s as the angles on a straight line are equal to 180 degrees. Okay, so great, we’ve now found two angles that we can. Let’s now move on to the measure of the angle that we’re looking to find. And that’s the angle 𝐴𝐶𝐷.
So I’m gonna mark this now on our diagram. So we’ve got angle 𝐴𝐶𝐷 is the one that we’re actually looking for. So it’s now that we can actually use some notation on our diagram to help us work out what angle 𝐴𝐶𝐷 is actually gonna be equal to cause we got these two arrows here. And they tell us that actually these two lines are parallel. So now, if I draw a little sketch of parallel lines, we can see two angles here that are gonna be the same. And they’re gonna be the same because, in fact, they’re alternate angels. And we know that alternate angles on parallel lines are, in fact, equal to each other.
Okay, so now we can use this to help us find out what the angle 𝐴𝐶𝐷 is actually equal to. Well, we can now see that angle 𝐴𝐶𝐷 is gonna be equal to angle 𝐵𝐴𝐶 plus angle 𝐵𝐴𝐸 because these two angles together make up our alternate angle which is alternate to angle 𝐴𝐶𝐷. So this is gonna be equal to 92 plus 35 which gives us an answer of 127 degrees. And again, we give our reason which we’ve already mentioned. And the reasoning behind this calculation is because they’re alternate angles on parallel lines. So, therefore, we can say, using the information that we’ve been given, we can say that the measure of angle 𝐴𝐶𝐷 is equal to 127 degrees.