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. BAC and BCA are the base angles of the triangle picture on the left. The congruent angles are called the base angles and the other angle is known as the vertex angle. In these kind of questions, you must give a reason for the angles that you found. An i sosceles triangle has two congruent sides and two congruent angles. 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 ???. Remember that the sum of angles of a triangle is. So therefore, we can say that the measure of angle ??? is equal to 52 degrees. In an isosceles triangle, the vertex angle is twice either base angle. And this is because, again, angles in a triangle add up to 180 degrees. 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. (Here a and b are the lengths of two sides and is the angle between these sides. And this is actually also equal to 64 degrees. In geometry, the isosceles triangle formulas are defined as the formulas for calculating the area and perimeter of an isosceles triangle. So next, we actually move on to angle ???. If we are given a base angle of say 45, we know the base angles are congruent (same measure) and the interior angles of any triangle always add to 180. 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 ???. And we know that because we actually have these markers on the diagram that show us that these two lengths are equal.
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 ???.