Two of the angles in a triangle are 70 degrees and 40 degrees. Jack says, “The triangle is equilateral.” Explain why Jack is not correct.
The first sentence in the problem tells us two of the angles inside a triangle. Remember, triangles have three angles. That’s why they’re called triangles. So two of those three angles are 70 degrees and 40 degrees. We’re also given another statement about the triangle. But we find out later on that this is not correct. Jack says that the triangle is equilateral. We’re told that Jack’s wrong, but why is he wrong?
The problem’s all about understanding what the word “equilateral” means and what an equilateral triangle is like. The clue to what an equilateral triangle is is in the name. On an equilateral triangle, all of its sides are the same length. And because all of its sides are equal, this means that the three angles inside the triangle are equal too.
This is the first reason why we know that Jack is not correct. The angles in the triangle that Jack is looking at are 70 degrees and 40 degrees. They’re different. The triangle can’t be equilateral. So we could answer the question by giving this as an explanation. Jack is not correct because equilateral triangles have three equal angles, but the angles in Jack’s triangle are different.
This is a very clear answer. But there’s one more fact that if we know it we could also include. It’s a fact that’s true of all triangles. The three angles inside every single triangle add up to 180 degrees. We’ve already said that an equilateral triangle has all angles the same. So we can calculate the angle inside an equilateral triangle by dividing 180 by three.
18 divided by three equals six. So 180 divided by three equals 60. Each of the three angles inside an equilateral triangle is 60 degrees. 60 plus 60 plus 60 equals 180. And so another way of answering the question is like this. The angles in an equilateral triangle are all 60 degrees, but the angles in Jack’s triangle are 70 degrees and 40 degrees.
So to understand how to answer the question, we needed to recognise what the word “equilateral” means. Equilateral triangles have all sides equal. But most importantly for this question, they have all angles equal. So why is Jack not right? Jack is not correct because equilateral triangles have three equal angles, but the angles in Jack’s triangle are different. The angles in an equilateral triangle are all 60 degrees, but the angles in Jack’s triangle are 70 degrees and 40 degrees.