Exploring Triangle Angle Theorems

The lecture covers the triangle sum theorem, proving that the sum of a triangle's interior angles is 180 degrees using the parallel postulate. It then applies this theorem to solve algebraic problems involving triangles. The exterior angle theorem is introduced, stating that an exterior angle equals the sum of the two non-adjacent interior angles. The lecture demonstrates this theorem with examples and solves related problems.

What does the Triangle Sum Theorem state?

• The sum of the interior angles of a triangle is equal to 180 degrees.

• The sum of the exterior angles of a triangle is equal to 360 degrees.

• The sum of the exterior angles of a quadrilateral is equal to 720 degrees.

• The sum of the interior angles of a quadrilateral is equal to 360 degrees.

Which postulate is used to prove the Triangle Sum Theorem?

• Angle Bisector Postulate

• Congruence Postulate

• Perpendicular Postulate

• Parallel Postulate

In the proof of the Triangle Sum Theorem, what type of angles are formed when a transversal intersects parallel lines?

• Alternate Interior Angles

• Corresponding Angles

• Supplementary Angles

• Vertical Angles

If angle J is represented by 3x, angle K by 2x + 40, and angle L by 60 - x, what is the value of x if the sum of these angles is 180 degrees?

• 40

• 30

• 20

• 10

What is the measure of angle J if x is found to be 20?

• 80 degrees

• 100 degrees

• 60 degrees

• 40 degrees

What does the Exterior Angle Theorem state?

• An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

• An exterior angle of a triangle is equal to the sum of the two adjacent interior angles.

• An exterior angle of a triangle is equal to the difference of the two non-adjacent interior angles.

• An exterior angle of a triangle is equal to the sum of all three interior angles.

In the proof of the Exterior Angle Theorem, which angles are considered a linear pair?

• Angle 2 and Angle 3

• Angle 1 and Angle 4

• Angle 1 and Angle 2

• Angle 3 and Angle 4

If the exterior angle is represented by 7x + 15 and the two non-adjacent interior angles are represented by 3x and x + 45, what is the value of x?

• 20

• 5

• 10

• 15

What is the measure of the exterior angle WXZ if x is found to be 10?

• 85 degrees

• 105 degrees

• 75 degrees

• 95 degrees

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

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees