Fill in the blank(s) to correctly complete each sentence.

Question

The sum of the measures of the angles of any triangle is ________________ .

Accepted Answer

Welcome back everyone. What is the sum of the angles? Xy and Z in a triangle? XYZ were given four answer choices. A 200 degrees B 360 degrees C 90 degrees and the 180 degrees. So to approach this problem, we have two options. One of the options is just to remember the sum of the angles in a triangle. It doesn't really matter what type of a triangle we have. If we draw any type of triangle, the sum of the three angles is always going to be the same. So let's suppose we have a triangle XYZ. There will be three angles, Xy and Z. And we can essentially remember that the sum of these angles always equates to 180 degrees. So that's one of the methods, but it's not universal. Essentially, we can just use a formula for the sum of angles in any polygon with N sides, which essentially corresponds to N minus two multiplied by 180 degrees. If we have a triangle that essentially has three sides, so N is equal to three right. And we can say that the sum of the angles XY and Z is going to be equal to. Now, our N is three. So we take three minus two multiplied by 180 degrees, which is 180 degrees. This formula works for any polygon, right. Essentially, if we have, let's say a hexagon, our N is going to be six, right? And that's it. For this specific problem, we have determined the final answer which corresponds to the answer choice, the 180 degrees. Thank you for watching.

Fill in the blank(s) to correctly complete each sentence.
The sum of the measures of the angles of any triangle is ________________ .

Key Concepts

Triangle Angle Sum Theorem

Interior Angles of a Triangle

Basic Angle Measurement

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