In this lesson, let’s learn about angle measures and equilateral, isosceles, and scalene triangles. The problem requires us to measure and find the measure of each of the variables given to us. Angles, certain angles have been marked as variables. We need to classify each triangle as either equilateral, isosceles, or scalene. So, let’s do them one by one.

Part A shows us a triangle where one of the angles is given to us is 54 degrees. The other two seem like they are equal because they are both marked with a variable P degrees. So, we’ve go the Triangle Sum Theorem which says that the sum of all angle measures of a triangle is 180 degrees. That’s what we’re going to use for each of these problems. So, if all three angles, some of them measure 180 degrees, what do I know? I know the 54 plus P plus P equals 180. 54 degrees plus P degrees, plus P degrees equals 180 degrees or 2p, P plus P is 2p plus 54 equals 180. If I want to subtract 54 from both sides to solve the equation, I get 2p equals 180 minus 54 is 126. If I want to divide both sides by two, we get P equals 126 by two is 63 or P degrees equals 63 degrees. So, the moment I know that P is 63 degrees and this is 63 degrees as well, I can see that two angles of this triangle are equal which means it is an isosceles triangle.

Let’s try the second one. The second one says, all three angles are the same variable A which means three times A equals 180 degrees, relatively simple. A plus A plus A is three times A equals 180 degrees. If I divide both sides by three, I get A equals 60 degrees. If A equals 60 degrees, then all three angles are 60 degrees which gives us that the triangle is actually an equilateral triangle. Equilateral triangles have all three angles equal or congruent.

Let’s look at the third part. Third part, we’re given the three angles are variables three times Y, four times Y and two times Y. So based on the triangle’s sum, we have 3y plus 4y plus 2y equals 180 degrees. Four plus seven plus two is nine so nine times Y degrees equals 180 degrees. All I did was combine the like terms which means if I divide both sides by nine, it gives me y equals 20 degrees. So, what is 2y is 20 times two is 40 degrees. Four times Y is four times 20 which is 80 degrees and this is 60 degrees. 80, 60, and 40 are the three measures. If all three angles of a triangle are different in measure, then it is a scalene triangle. All three angles are different.