In this page, we practice using the rule:
$$\text{Exterior angle}=\text{sum of the two remote interior angles}$$
Example 1
The two remote interior angles are:
$$80^\circ$$
and
$$30^\circ$$
Find the exterior angle.
Solution:
Using the Exterior Angle Theorem:
$$\text{Exterior angle}=80^\circ+30^\circ$$
$$\text{Exterior angle}=110^\circ$$
So, the exterior angle is:
$$110^\circ$$
Example 2
The exterior angle is:
$$60^\circ$$
One remote interior angle is:
$$40^\circ$$
The other remote interior angle is:
$$x$$
Find the missing remote interior angle \(x\).
Solution:
Using the Exterior Angle Theorem:
$$x+40^\circ=60^\circ$$
$$x=20^\circ$$
So, the missing remote interior angle is:
$$x=20^\circ$$
Example 3
The exterior angle is:
$$100^\circ$$
The two remote interior angles are:
$$x$$
and
$$x$$
Find \(x\), the measure of each remote interior angle.
Solution:
Using the Exterior Angle Theorem:
$$x+x=100^\circ$$
$$2x=100^\circ$$
$$x=50^\circ$$
So, each remote interior angle is:
$$50^\circ$$
Example 4
The exterior angle is:
$$120^\circ$$
One remote interior angle is:
$$50^\circ$$
The other remote interior angle is:
$$x$$
Find the missing remote interior angle \(x\).
Solution:
Using the Exterior Angle Theorem:
$$50^\circ+x=120^\circ$$
$$x=70^\circ$$
So, the missing remote interior angle is:
$$x=70^\circ$$
Example 5
The exterior angle is:
$$7x$$
The two remote interior angles are:
$$2x+3^\circ$$
and
$$6x-13^\circ$$
Find \(x\), then find the two remote interior angles and the exterior angle.
Solution:
Using the Exterior Angle Theorem:
$$(2x+3^\circ)+(6x-13^\circ)=7x$$
$$8x-10^\circ=7x$$
$$x=10^\circ$$
Now find the angles.
First remote interior angle:
$$2(10^\circ)+3^\circ=23^\circ$$
Second remote interior angle:
$$6(10^\circ)-13^\circ=47^\circ$$
Exterior angle:
$$7(10^\circ)=70^\circ$$
Check:
$$23^\circ+47^\circ=70^\circ$$
So, the two remote interior angles are:
$$23^\circ \text{ and } 47^\circ$$
and the exterior angle is:
$$70^\circ$$
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)