Understanding the Exterior Angle Theorem | Explaining the Relationship between Exterior and Remote Interior Angles of a Triangle

A measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

In a triangle, an exterior angle is an angle formed by one side of the triangle and the extension of another side

In a triangle, an exterior angle is an angle formed by one side of the triangle and the extension of another side. The remote interior angles are the two angles inside the triangle that are not adjacent to the exterior angle.

Let’s suppose we have a triangle with vertices A, B, and C, and an exterior angle formed at vertex A. We can call the measure of the exterior angle as angle x. The remote interior angles can be denoted as angle B and angle C.

The statement “A measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles” means that angle x is equal to the sum of angles B and C.

Mathematically, we can express this relationship as:

x = B + C

This relationship is known as the Exterior Angle Theorem. According to this theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

For example, if angle B is 40 degrees and angle C is 50 degrees, then the measure of the exterior angle x would be:

x = B + C
x = 40 + 50
x = 90

Therefore, the measure of the exterior angle x is 90 degrees, which is equal to the sum of angles B and C.

Remember that this relationship holds true for any triangle, regardless of its size or shape.

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