Interior and Exterior Angle Theorem

Exterior angles of a triangle day 2

Interior angles are on the inside of the triangle.

Exterior angles are on the outside of the triangle attached to a vertex.

Refresher:

The interior angles of a triangle add up to 180⁰

The exterior angle of a triangle is the sum of the 2 interior angles that are not next to it.

Multiple Choice

How do we solve for x?

• 50 + 70 + a = 180

• 70 - 50 = a

• 70 - 50 + 180 = a

Multiple Choice

On the last slide, we created the equation 50 + 70 + a = 180.

Now solve for x

• x = 120

• x = 20

• x = 60

Exterior angles

Remember there are 2 exterior angles at each vertex.

Exterior angle

We add the 2 interior angles that are NOT next to the exterior angle to find the exterior angle

Multiple Choice

Set up the equation to find the exterior angle.

• 75 + 36 + x = 180

• 75 + 36 = x

• 75 - 36 - x

Fill in the Blanks

Exterior angles

Sometimes we have the exterior angle and we need to find the missing interior angle.

To do this, we SUBTRACT the interior angle from the exterior. We can do this because

x + 80 = 145

Multiple Choice

Solve for x

• x = 65

• x = 225

• x = 100

Exterior angles

If algebra is involved, we MUST write an equation to solve.

The equation will be:

(5y + 3) + (4y + 8) = 146

(we add the 2 interior angles and the sum will equal the exterior angle)