Q:

Why do the angles in a triangle add up to 180 degrees?

A:

The three interior angles of a triangle always add up to 180 degrees, which is one of the identifying characteristics of a triangle. Each shape has properties that are unique to that specific figure. Other identifying properties are that the exterior angles of a trangle always add up to 360 degrees and that a triangle always has three sides.

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Many combinations of angle can be used to meet the 180 degree requirement. An obtuse triangle has one obtuse angle (an angle that measures between 90 and 180 degrees) and two acute angles (angles that measure less than 90 degrees). A right angle triangle has a single 90 degree angle and two acute angles. The acute triangle is composed of three acute angles.

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A scalene triangle has no equal sides. There is no word for a triangle with three different angle sizes. The words describing angle sizes — right, obtuse and acute — reference the degrees of the angle, not their relationships to one another.

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The sum of the interior angles of a pentagon is 540 degrees. Each of the five interior angles of a regular pentagon measures 108 degrees.

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When the lengths of all sides of a triangle are added, the result is called the perimeter of the triangle. In general, a perimeter is the distance of the curve that borders a lamina or a two-dimensional closed planar surface. Half of a triangle's perimeter is called the semiperimeter.