Exploring the Exterior Angle Sum Theorem in Triangles

This tutorial covers the exterior angle theorem, explaining how the exterior angle of a triangle is equal to the sum of the two opposite interior angles. It provides examples and problem-solving exercises, including algebraic applications, to help students understand and apply the theorem effectively.

What is the sum of all interior angles in a triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

An exterior angle of a triangle is supplementary to which angle?

• Any interior angle

• The adjacent interior angle

• None of the above

• The opposite interior angle

According to the Exterior Angle Theorem, the exterior angle is equal to:

• The product of the two opposite interior angles

• The difference between the two opposite interior angles

• The sum of the two opposite interior angles

• The sum of the adjacent interior angles

If an exterior angle is 120 degrees and one of the opposite interior angles is 30 degrees, what is the other opposite interior angle?

• 150 degrees

• 120 degrees

• 90 degrees

• 60 degrees

In a triangle, if one interior angle is 30 degrees and the exterior angle adjacent to it is 150 degrees, what is the measure of the other two interior angles?

• 60 degrees and 90 degrees

• 45 degrees and 105 degrees

• 60 degrees and 120 degrees

• 75 degrees and 75 degrees

Solve for X: If X is an exterior angle and the opposite interior angles are 40 degrees and 60 degrees, what is X?

• 100 degrees

• 140 degrees

• 90 degrees

• 120 degrees

If an exterior angle is represented by 8 + 6X and the sum of the opposite interior angles is 4X + 32, what is the value of X?

• 4

• 6

• 2

• 8

In a triangle, if the exterior angle is 140 degrees and one of the opposite interior angles is 50 degrees, what is the other opposite interior angle?

• 30 degrees

• 40 degrees

• 60 degrees

• 50 degrees

If the exterior angle is 2X + 10 and the opposite interior angles are X + 20 and X + 30, what is the value of X?

• 10

• 20

• 40

• 30

What is the measure of an exterior angle if the opposite interior angles are 3X and 2X + 10, and X is 20?

• 130 degrees

• 110 degrees

• 90 degrees

• 70 degrees