The proof comes from the fact that the three angles in a triangle add up to 180 degrees. An right triangle has only one right angle – the other two angles are acute angles, with measures less than 90 degrees (as mentioned earlier, their measures must add up to 90 degrees, since they are complementary angles). Can A Triangle Have Two Right Angles?Ī triangle cannot have two (or three) right angles. Note that the other two angles in a right triangle can be equal, but they do not have to be. Without a 90 degree angle, we cannot use the Pythagorean Theorem (instead, we must use the Law of Cosines). Remember that if the side lengths of a right triangle are a, b, and c (with c the hypotenuse, or the longest side, across from the 90 degree angle), then: It also means that the other two angles (across from the legs) are complementary angles (they add up to 90 degrees).įor a right triangle, we can use the Pythagorean Theorem. This means that the two shortest sides (legs) of the right triangle are perpendicular to one another. An obtuse angle is an angle with a measure of more than 90 degrees.Ī right triangle has one right angle (and only one) with a measure of exactly 90 degrees. When Is A Triangle Obtuse?Ī triangle is obtuse when it has an obtuse angle. To answer this question, we’ll start by looking at obtuse triangles. However, this still leaves the question of how many such angles the triangle can have. As you can see from some of these examples, a triangle can have an angle greater than or equal to 90 degrees. Three 60 degree angles (equilateral triangle).A 90 degree angle and two 45 degree angles (right isosceles triangle).A 40 degree angle and two 70 degree angles (isosceles triangle).Angles of 50 degrees, 60 degrees, and 70 degrees (acute triangle).Angles of 30 degrees, 60 degrees, and 90 degrees (right triangle).Angles of 10 degrees, 20 degrees, and 150 degrees (obtuse triangle).For example, we could have a triangle with: This restriction still leaves lots of possibilities for the angles in a triangle. This article from Home School Math has a nice proof of this fact! The angles in a triangle always add up to 180 degrees: no more, no less. No matter the shape of a triangle, its three angles will always add up to the same value.Īngle in standard position What Do The Angles In A Triangle Add Up To? The longest side will be across from the largest angle, and the smallest side will be across from the smallest angle. Each of the sides is “across from” one of the angles. We’ll also answer some common questions about triangles and what type of angles they can have.Ī triangle is a polygon that always has exactly three sides and three angles. In this article, we’ll take a closer look at triangles and their angles. For example, the largest angle of a triangle will be across from its longest side. Of course, comparing the angles of triangles can also tell us about the sides. Equilateral triangles have three sides (and angles) that are the same. Isosceles triangles have two sides (and angles) that are the same. A triangle has either two or three acute angles. Triangles can have at most one right or obtuse angle. We can use their angles to categorize triangles and make statements about what they look like and how their sides are related.Ī triangle’s angles sum to 180 degrees. Triangles come up often in mathematics, and for good reason – they are useful for a variety of purposes.
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