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Video: Types of Triangles

Bethani Gasparine

If the 𝑚∠𝐴 = 56°, 𝑚∠𝐵 = 66°, and 𝑚∠𝐶 = 58°, what is the type of △𝐴𝐵𝐶 in terms of the measures of the angles?

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Video Transcript

If the measure of angle 𝐴 is equal to 56 degrees and the measure of angle 𝐵 is equal to 66 degrees and the measure of angle 𝐶 is equal to 58 degrees, what is the type of triangle 𝐴𝐵𝐶 in terms of the measures of the angles?

Here we have triangle 𝐴𝐵𝐶. We know the measure of angle 𝐴 is equal to 56 degrees, the measure of angle 𝐵 is equal to 66 degrees, and the measure of angle 𝐶 is equal to 58 degrees. So we’re classifying this triangle based on the measure of the angles. So there are three options: it will either be an acute triangle, an obtuse triangle, or a right triangle.

In an acute triangle, all angle measures will be less than 90 degrees. And in an obtuse triangle, there will be one angle measure that is greater than 90 degrees. So it will be more than 90 degrees. And in a right triangle, there would be one angle measure that is equal to 90 degrees.

So here are our three angle measures: 56 degrees is less than 90 degrees, 66 degrees is less than 90 degrees, and 58 degrees is less than 90 degrees. So all three angle measures were less than 90 degrees. Therefore, triangle 𝐴𝐵𝐶 must be an acute triangle.