In this page, we practice using the idea that:
$$\text{Each exterior angle}=180^\circ-\text{ interior angle}$$
So, the two exterior angles at the same vertex are equal.
Example 1
The interior angle is:
$$60^\circ$$
Find both exterior angles.
Solution:
Each exterior angle forms a linear pair with the interior angle:
$$\text{Exterior angle}=180^\circ-60^\circ$$
$$\text{Exterior angle}=120^\circ$$
So, both exterior angles are:
$$120^\circ$$
Example 2
The interior angle is:
$$80^\circ$$
Find both exterior angles.
Solution:
$$\text{Exterior angle}=180^\circ-80^\circ$$
$$\text{Exterior angle}=100^\circ$$
So, both exterior angles are:
$$100^\circ$$
Example 3
The interior angle is:
$$x$$
Each exterior angle is:
$$x+40^\circ$$
Find \(x\), then find the interior angle and the exterior angles.
Solution:
The interior angle and an exterior angle form a linear pair:
$$x+(x+40^\circ)=180^\circ$$
$$2x+40^\circ=180^\circ$$
$$2x=140^\circ$$
$$x=70^\circ$$
So, the interior angle is:
$$70^\circ$$
Each exterior angle is:
$$70^\circ+40^\circ=110^\circ$$
Therefore, both exterior angles are:
$$110^\circ$$
Example 4
The interior angle is:
$$50^\circ$$
Each exterior angle is:
$$2x+30^\circ$$
Find \(x\), then find both exterior angles.
Solution:
First find the exterior angle using the interior angle:
$$\text{Exterior angle}=180^\circ-50^\circ$$
$$\text{Exterior angle}=130^\circ$$
Now use:
$$2x+30^\circ=130^\circ$$
$$2x=100^\circ$$
$$x=50^\circ$$
So, both exterior angles are:
$$130^\circ$$
Example 5
The interior angle is:
$$x$$
Each exterior angle is:
$$2x-20^\circ$$
Find \(x\), then find the interior angle and the exterior angles.
Solution:
The interior angle and an exterior angle form a linear pair:
$$x+(2x-20^\circ)=180^\circ$$
$$3x-20^\circ=180^\circ$$
$$3x=200^\circ$$
$$x=\frac{200}{3}^\circ$$
$$x\approx66.67^\circ$$
So, the interior angle is approximately:
$$66.67^\circ$$
Each exterior angle is:
$$180^\circ-66.67^\circ \approx 113.33^\circ$$
Therefore, both exterior angles are approximately:
$$113.33^\circ$$
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)