In a triangle, we can form exterior angles by extending the sides of the triangle.
At each vertex, there are actually two possible exterior angles, depending on which side we extend.
In this lesson, we will prove that these two exterior angles at the same vertex are equal.
Key Idea
When we extend both sides of a triangle at the same vertex, the two exterior angles formed are opposite angles, also called vertical angles.
Vertical angles are always equal.
Rule
At any vertex of a triangle:
The two exterior angles formed are equal because they are vertical angles.
Proof Idea
Extend both sides of a triangle at the same vertex.
This creates two exterior angles that are opposite each other.
These angles form a pair of vertical angles, and vertical angles are always equal.
Therefore, the two exterior angles at a vertex are equal.
Example
If one exterior angle at a vertex is \(120^\circ\), find the other exterior angle.
Since the two exterior angles are equal:
$$\text{The second exterior angle } = 120^\circ$$
Video Explanation
Practice
Continue Learning
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