Video: The Possible Types of the Interior Angles of a Triangle

Is it possible to draw a triangle with two obtuse angles?

02:27

Video Transcript

Is it possible to draw a triangle with two obtuse angles?

We need to think about a few things to answer this question. First, what is an obtuse angle? An obtuse angle is an angle measuring more than 90 degrees. We also need to know something about a triangle. Inside a triangle, all the angles add up to 180 degrees. Angle one plus angle two plus angle three equals 180 degrees in every triangle.

Could we draw an obtuse angle plus an obtuse angle plus a third angle that equals 180 degrees? Let’s try it. Here is an obtuse angle. It measures 92 degrees, only slightly larger than a right angle. Our first angle 92 degrees plus- we’ll need a second angle. This angle is 91 degrees. If we add 92 and 91, it equals 183 degrees. 183 degrees is larger than 180 degrees.

There’s a big gap in our shape though we’ve drawn one, two, three lines. And we have two obtuse angles. We cannot connect them. There is a space. This is because it is impossible to draw a triangle with two obtuse angles. The three lines would never connect.

The answer to the question, is it possible to draw a triangle with two obtuse angles is no. That is not possible. A triangle can only ever have one obtuse angle.

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