And this was because the angles in a triangle all added to 180 degrees. An example of this is our final angle, where we said that angle ??? was equal to 180 degrees minus 64 degrees minus 64 degrees which was equal to 52 degrees. In these kind of questions, you must give a reason for the angles that you found. The key thing to remember is that at each of our stages, we actually gave a reason. Just a quick recap of what we did, is we actually worked in stages to find different angles that we needed to allow us to work out the final angle of ???. It is given that the base angles of an isosceles triangle are equal and the vertex angle of an isosceles. So therefore, we can say that the measure of angle ??? is equal to 52 degrees. Let x be the base angle of an isosceles triangle.
A median of a triangle is a line from any vertex to the midpoint of the. And this is because, again, angles in a triangle add up to 180 degrees. An exterior angle of a triangle is an angle outside the triangle formed by one. And this is gonna be equal to 180 minus 64 minus 64, which is therefore equal to 52 degrees. And this is the one that the question’s looking for. And therefore, the two angles ??? and ??? must be equal. And this is because triangle ??? is isosceles. And this is actually also equal to 64 degrees. So next, we actually move on to angle ???. And we can actually see that the angles there, 116 and 64, are both on a straight line. And we get this because the angles on a straight line add up to 180.
And this is gonna be equal to 180 minus 116, which is equal to 64 degrees. The next angle we’re taking a look at is angle ???. So as you’ve seen, we’ve said one is because of a triangle being isosceles and the other one is angles in a triangle. And it’s actually worth noting at this point that when you’re calculating missing angles in a problem like this, you must give the reasoning for each angle. And this is because the angles in a triangle add up to 180 degrees. And this is gonna be equal to 180 minus 32 minus 32, which is equal to 116 degrees. Well, the next angle we’re gonna take a look at is angle ???. Let’s get on and find some more to help us find the angle that we’re looking for, which is ???. As the interior angle is acute, it is less than 90, the exterior angle must be greater than 90 and obtuse. This means that the interior and exterior angles at vertex must sum to 180. And we know that because we actually have these markers on the diagram that show us that these two lengths are equal. We know that angles on a straight line sum to 180 degrees. And the reason it’s equal to 32 degrees because triangle ??? is actually an isosceles triangle. And this is gonna be equal to 32 degrees. First of all, we could take a look at angle ???.