moomoomath logo header
lime green horizontal line
Welcome to MooMooMath
Quick Math Homework Help
Geometry Coach
geometry coach lesson plans
Can the exterior angles of a triangle be acute?

Yes  If the interior angle of the triangle is obtuse then the outside angle will be acute. Conversely, if the interior angle is acute then the exterior angle of the triangle will be obtuse.

Find measure ∠A and ∠C

m∠A + m∠B+m∠C =180°

36 + x + (x + 4) = 180
40 + 2x = 180
2x = 140
x = 70 = m∠A
x + 4 = 74 = m∠B

X +4
Exterior Angle of a Triangle
exterior angle of a triangle with 45 and 90 degree
exterior angle of a triangle with a  45 degree
triangle exterior angle theorem
video absolute value
horizontal line

Exterior Angle Formula

horizontal line

Exterior angles of a triangle

∠ A
Find the measure of the exterior angle A

Step 1. Extend out a line from the adjacent side.

Step 2.180-45 =135°

Step 3. The measure of angle a = 135°
∠ D
Find the measure of the exterior angle D

Step 1. Plug the given angle measurements into the exterior angle measure formula

m∠D= m∠B+m∠C 

45 + 90 = 135°

Step 2. The measure of angle D = 135°
​The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
The measure of an exterior angle of a triangle is greater than either of the two remote interior angles.

​The measure of the exterior angle is  supplementary to the interior angle. 

linear pair of angles with a triangle
measure of exterior angle
interior and exterior angles of a triangle illustrated
The Exterior Angle is the angle between one side of a triangle, and a line extended from the adjacent side.
 Exterior Angle .
Interior Angle .

What is an exterior angle?

triangle with the rmote interior angles highlighted
Exterior Angle
Remote Interior Angles

Remote Interior Angles

The remote interior angles of a triangles are the two angles that are not adjacent to the exterior angle.The remote interior angles do not share the vertex of the exterior angle.

The measure of the Exterior Angle is equal to the sum measure of the remote interior angles
Hi Welcome to MooMooMath. Today we are going to look at the measure of the exterior angle of a triangle. We have a triangle right here and we only know one angle. Which angles of the triangle are the exterior angles and which are the interior angles? The interior angles are the three angles on the inside of the triangle. To create an exterior angle, I will go to the vertex, and I’m going to extend this side out. This creates an exterior angle that is associated with this 45 degree interior angle, and we know lines add up to 180. So these two add up to what we call a linear pair, they are supplementary, so I can find this exterior angle measure by taking 180 and subtracting 45 so we end up with 135 degrees. It is an obtuse angle so this angle is 135 degrees. So let’s look at the rules for finding exterior angles in a triangle. First, you have to create the exterior angle by extending one side of the triangle. Next, the measure is supplementary to the interior angle. For example, the interior angle is 30, we extend this side out creating an exterior angle, and we find the measure of the angle by subtracting 180 -30 =150. Therefore, we have a 150 degree exterior angle. Hope this was helpful.