In this page, we practice using the idea that:
Two exterior angles at the same vertex are equal.
Example 1
One exterior angle is:
$$100^\circ$$
Find the other exterior angle.
Solution:
Since the two exterior angles are equal:
$$\text{Other exterior angle}=100^\circ$$
So, the other exterior angle is:
$$100^\circ$$
Example 2
One exterior angle is:
$$75^\circ$$
Find the other exterior angle.
Solution:
Since the two exterior angles are equal:
$$\text{Other exterior angle}=75^\circ$$
So, the other exterior angle is:
$$75^\circ$$
Example 3
One exterior angle is:
$$90^\circ$$
The other exterior angle is:
$$x+20^\circ$$
Find \(x\).
Solution:
Since the two exterior angles are equal:
$$x+20^\circ=90^\circ$$
$$x=70^\circ$$
So:
$$x=70^\circ$$
The two exterior angles are both:
$$90^\circ$$
Example 4
One exterior angle is:
$$x$$
The other exterior angle is:
$$2x-30^\circ$$
Find \(x\).
Solution:
Since the two exterior angles are equal:
$$x=2x-30^\circ$$
$$x=30^\circ$$
So:
$$x=30^\circ$$
Therefore, the two exterior angles are both:
$$30^\circ$$
Example 5
One exterior angle is:
$$3x$$
The other exterior angle is:
$$x+40^\circ$$
Find \(x\), then find the measure of each exterior angle.
Solution:
Since the two exterior angles are equal:
$$3x=x+40^\circ$$
$$2x=40^\circ$$
$$x=20^\circ$$
Now find each exterior angle:
$$3x=3(20^\circ)=60^\circ$$
and
$$x+40^\circ=20^\circ+40^\circ=60^\circ$$
So, the two exterior angles are both:
$$60^\circ$$
Practice
- More Examples (Current page)
Continue Learning
- Sum of Exterior Angles of a Triangle (Proof)
- Exterior Angle Theorem of a Triangle
- Two Exterior Angles at a Vertex are Equal (Proof)
- Two Exterior Angles are Equal at a Vertex (Quick Proof)