Question

What is the measure of one exterior angle of a regular triangle?

Short answer

The measure of one exterior angle of a regular triangle is 120 degrees.

Step-by-step solution

Understand the properties of a regular triangle

A regular triangle is also known as an equilateral triangle. This means all its sides are the same length, and all its interior angles are equal. Since the sum of interior angles in any triangle is 180 degrees, each interior angle of an equilateral triangle measures 60 degrees.

Use the exterior angle theorem

The exterior angle of a triangle is formed by one side of the triangle and the extension of another side. It is equal to the sum of the two non-adjacent interior angles, but in a regular triangle scenario, since all angles are equal, a simpler rule can be used: each exterior angle is supplementary to its respective interior angle (i.e., they add up to 180 degrees).

Calculate the exterior angle

Since each interior angle of a regular triangle is 60 degrees, the exterior angle, which is supplementary to the interior angle, is calculated by subtracting the interior angle from 180 degrees: \(180 - 60 = 120\) degrees.

Conclusion

The measure of one exterior angle of a regular triangle, or equilateral triangle, is 120 degrees using the property that it is supplementary to the 60-degree interior angle.

Key concepts

Equilateral Triangle

An equilateral triangle is a special type of triangle where all three sides have equal length. This uniformity extends to the angles as well, meaning each interior angle in an equilateral triangle is equal. - Each interior angle measures 60 degrees. - The triangle is perfectly symmetrical, making it a popular choice in geometric design. Because all sides and angles are equal, equilateral triangles have unique properties that simplify many calculations, such as finding exterior angles.

Interior Angle Sum

The interior angle sum theorem is a fundamental principle when working with triangles. It states that the sum of all the interior angles in any triangle is always 180 degrees, regardless of the triangle's shape. - For an equilateral triangle, this divides evenly among the three angles, so each angle is 60 degrees. - This rule applies to all triangles, whether they are equilateral, isosceles, or scalene. Understanding this theorem helps in various calculations, such as determining unknown angles in different types of triangles. If you know two angles, you can always find the third by subtracting the sum of the known angles from 180 degrees.

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. This concept plays a vital role in understanding exterior angles of polygons, especially triangles. - In triangles, an exterior angle is formed by extending one of its sides.- The exterior angle and the adjacent interior angle are supplementary.For an equilateral triangle, where each interior angle measures 60 degrees, the exterior angle directly supplements it to reach 180 degrees.For example, if the interior angle is 60 degrees, the exterior angle is calculated as follows:\[180 - 60 = 120\]