The measure of a(n)_____ of a triangle is equal to the sum of the measures of its two remote interior angles.
The measure of a(n) exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
The measure of a(n) exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
To find the missing word and understand the concept explained in the question, we need to recall some basic principles of geometry.
In a triangle, the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles.
In this case, the word we are looking for is "exterior angle."
To understand why, let's break it down step by step:
1. Start with a triangle.
2. Select one of its vertices (corners) and draw a line that extends beyond one of the triangle's sides. This line is the extension of that side.
3. The angle formed between the extension of the side and the adjacent side of the triangle is called the exterior angle.
4. The two interior angles that are not adjacent to the exterior angle are known as the remote interior angles.
Now, if we sum up the measures of the two remote interior angles, we will find that this sum is equal to the measure of the exterior angle.