More Examples – Sum of Exterior Angles of a Triangle
In this page, we practice using the rule:
$$\text{Sum of exterior angles}=360^\circ$$
Example 1
Find the missing exterior angle \(x\).
The exterior angles of the triangle are:
\(100^\circ,\quad 120^\circ,\quad x\)
Using the sum of the exterior angles:
$$100^\circ+120^\circ+x=360^\circ$$
$$220^\circ+x=360^\circ$$
x=140^\circ$$
So, the missing exterior angle is:
$$x=140^\circ$$
Example 2
Find the missing exterior angle \(x\).
The exterior angles of the triangle are:
\(90^\circ,\quad 150^\circ,\quad x\)
Using the sum of the exterior angles:
$$90^\circ+150^\circ+x=360^\circ$$
$$240^\circ+x=360^\circ$$
x=120^\circ$$
So, the missing exterior angle is:
$$x=120^\circ$$
Example 3
Find \(x\).
The exterior angles of the triangle are:
\(x,\quad x,\quad 120^\circ\)
Using the sum of the exterior angles:
$$x+x+120^\circ=360^\circ$$
$$2x+120^\circ=360^\circ$$
$$2x=240^\circ$$
$$x=120^\circ$$
So:
$$x=120^\circ$$
Therefore, the three exterior angles are:
$$120^\circ,\quad120^\circ,\quad120^\circ$$
Example 4
Find \(x\).
The exterior angles of the triangle are:
\(x,\quad2x,\quad x\)
Using the sum of the exterior angles:
$$x+2x+x=360^\circ$$
$$4x=360^\circ$$
$$x=90^\circ$$
So:
$$x=90^\circ$$
Therefore, the three exterior angles are:
$$90^\circ,\quad180^\circ,\quad90^\circ$$
Example 5
Find \(x\).
The exterior angles of the triangle are:
\(x,\quad3x,\quad2x\)
Using the sum of the exterior angles:
$$x+3x+2x=360^\circ$$
$$6x=360^\circ$$
$$x=60^\circ$$
So:
$$x=60^\circ$$
Therefore, the three exterior angles are:
$$60^\circ,\quad180^\circ,\quad120^\circ$$
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)