Which theorem states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle?
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The theorem you are referring to is called the Exterior Angle Theorem.
To prove the Exterior Angle Theorem, you need to know a few concepts and properties related to angles in a triangle. Let's break it down step by step:
Step 1: Understand the terminologies
An exterior angle is the angle formed by one side of a triangle and the extension of its adjacent side.
A remote interior angle is an angle inside the triangle that is not adjacent to the exterior angle.
Step 2: Identify the angles involved
In a triangle, there are three interior angles and one exterior angle related to each vertex.
Step 3: Observe the relationships
When you have an exterior angle of a triangle, it is always equal to the sum of the two remote interior angles.
Step 4: Express it as an equation
You can express the Exterior Angle Theorem as:
Measure of the exterior angle = Measure of remote interior angle 1 + Measure of remote interior angle 2
Step 5: Understand the reasoning
The reason behind this theorem is based on a property of a straight line. It states that the sum of the measures of the two interior angles on the same side of the transversal, intersected by a pair of parallel lines, is equal to 180 degrees. Since the exterior angle and each remote interior angle form a straight line, their measures must add up to 180 degrees.
To use the Exterior Angle Theorem, you need to know the measures of the two remote interior angles. Then, you can find the measure of the exterior angle by adding them together.