What is the sum of the interior angles of any triangle?

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Multiple Choice

What is the sum of the interior angles of any triangle?

In any triangle, the interior angles add up to 180 degrees. A quick way to see why is to draw a line through the top vertex parallel to the base. The angles at the base of the triangle become equal to the two angles formed where this parallel line meets the sides. Those three angles—the top angle and the two angles along the base—lie on a straight line, which measures 180 degrees. Since those three interior angles fill up a straight angle, their sum must be 180 degrees. So 180 degrees is the sum for any triangle. The numbers 90, 270, or 360 don’t fit because you can’t have a triangle whose interior angles add to those values with positive angles in a plane.

In any triangle, the interior angles add up to 180 degrees. A quick way to see why is to draw a line through the top vertex parallel to the base. The angles at the base of the triangle become equal to the two angles formed where this parallel line meets the sides. Those three angles—the top angle and the two angles along the base—lie on a straight line, which measures 180 degrees. Since those three interior angles fill up a straight angle, their sum must be 180 degrees.

So 180 degrees is the sum for any triangle. The numbers 90, 270, or 360 don’t fit because you can’t have a triangle whose interior angles add to those values with positive angles in a plane.

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