Exterior Angle of Triangle

The exterior angles of a triangle are those angles that are formed outside it. In other words, the exterior angle of a triangle is the angle that is formed between one of its sides and its adjacent extended side. Let us learn more about the exterior angle of triangle in this article.

When any side of a triangle is extended, the angle that is formed with this side and its adjacent side is called the exterior angle of a triangle. There are three exterior angles in a triangle. It should be noted that each exterior angle forms a linear pair with its corresponding interior angle. We know that the interior angle of a triangle is formed inside it where the sides meet at a vertex. Observe the following figure to distinguish between the interior angles and the exterior angles of a triangle.

We can see that each interior angle forms a linear pair with its corresponding exterior angle. This means that the sum of each exterior angle and its respective interior angle is equal to 180°.

There are three basic properties of the exterior angles of a triangle.

• In a triangle, each exterior angle and its corresponding interior angle form a linear pair of angles. This means that the sum of the interior and exterior angle is equal to 180°.
• The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). This is also known as the Exterior Angle theorem.
• The sum of all the exterior angles of a triangle is 360°.

Based on the properties of the exterior angles, the following formulas can be used to find the exterior angles of a triangle. Referring to the triangle given below, the formulas can be understood in a better way.

• Each Exterior angle = 180 - Interior angle. Here, ∠e = 180 - ∠b. Similarly, ∠d = 180 - ∠c, and ∠f = 180 - ∠a
• Exterior angle = Sum of Interior opposite angles. Here, ∠d = ∠a + ∠b, ∠f = ∠b + ∠c, and ∠e = ∠a + ∠c
• Sum of the Exterior angles of a triangle = 360°. Here, ∠d + ∠e + ∠f = 360°

Related Links

Check out the links given below related to the exterior angles of a triangle.

• Interior angles
• Exterior Angles of a Polygon
• Exterior Angle Theorem
• Linear Pair of Angles

What is the Exterior Angle of Triangle?

The exterior angle of a triangle is the angle that is formed with one side and the adjacent extended side of a triangle. There are 3 exterior angles in a triangle and the sum of the exterior angles of a triangle is always equal to 360°.

How to Find the Exterior Angle of Triangle?

The value of the exterior angle of a triangle can be calculated using various formulas depending on the other known angles. The following formulas can be used according to the given parameters.

• Each Exterior angle = 180° - Interior angle. This formula can be used if the corresponding interior angle is given.
• Exterior angle = Sum of Interior opposite angles. This formula can be used to find the exterior angle when its remote interior opposite angles are given.
• The sum of all the exterior angles of a triangle is 360°. This formula can be used to find the unknown value of an exterior angle when the other two exterior angles are given.

What is the Sum of Exterior Angles of a Triangle?

The sum of the exterior angles of a triangle is always equal to 360°. This property applies to all polygons, which means that the sum of the exterior angles of all polygons is 360°.

How to find the Missing Exterior Angle of a Triangle?

A missing exterior angle of a triangle can be calculated using any of the following formulas. This depends on the angles that are given in the question.

• The first formula to find the exterior angle can be used if the corresponding interior angle is given. Each Exterior angle = 180 - Interior angle.
• The second formula can be used to find the exterior angle when its interior opposite angles are given. Exterior angle = Sum of Interior opposite angles.
• The third formula can be used to find the unknown value of an exterior angle when the other two exterior angles are given. The sum of all the exterior angles of a triangle is 360°.

Are the Exterior Angles of a Triangle Equal to 360°?

Yes, the sum of the exterior angles of a triangle is always equal to 360°.

Are the Exterior Angles of a Triangle Always Obtuse?

No, the exterior angles of a triangle may not always be obtuse (more than 90°). However, the sum of all the three exterior angles should always be 360°. For example, if two exterior angles of a triangle are 165° (obtuse) and 141° (obtuse), the third one is 54° (acute).

What is the Measure of Each Exterior Angle of an Equilateral Triangle?

The measure of each exterior angle of an equilateral triangle is 120°. An equilateral triangle is a triangle in which all the sides are equal in length and all the 3 interior angles are of equal measure. This means each interior angle of an equilateral triangle is 60° because the sum of the interior angles is 180°. Now, if each interior angle of an equilateral triangle is 60°, its corresponding exterior angle will be 120°. This is because in a triangle, the exterior angle and its corresponding interior angle form a linear pair of angles. This means that the sum of the interior and exterior angle is equal to 180°.

What is the Exterior Angle Theorem of a Triangle?

According to the exterior angle theorem, the measure of an exterior angle is equal to the sum of the interior opposite angles (remote interior angles). This means if we need to find the exterior angle of a triangle, and its remote interior angles are known, then the value of the exterior angle will be the sum of those two interior opposite angles.