Exploring Triangle Sum and Exterior Angle Theorems

This video tutorial covers two important theorems in geometry: the Triangle Sum Theorem and the Exterior Angle Theorem. It begins with a review of different types of triangles and their properties. The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees, regardless of the triangle's shape. The Exterior Angle Theorem explains that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. The video provides examples to illustrate how these theorems can be applied to solve problems involving triangles.

What is the definition of an acute triangle?

• One interior angle is 90 degrees.

• One interior angle is greater than 90 degrees.

• All sides are of different lengths.

• All interior angles are less than 90 degrees.

Which type of triangle has two sides of equal length?

• Equilateral

• Right

• Isosceles

• Scalene

What does the Triangle Sum Theorem state?

• The sum of the interior angles is 360 degrees.

• The sum of the exterior angles is 360 degrees.

• The sum of the interior angles is 180 degrees.

• The sum of the remote interior angles is equal to the exterior angle.

In a right triangle with one angle of 90 degrees and another of 20 degrees, what is the measure of the third angle?

• 90 degrees

• 80 degrees

• 70 degrees

• 60 degrees

If an isosceles triangle has one angle of 50 degrees, what is the measure of the other two angles?

• 50 degrees and 80 degrees

• 50 degrees and 50 degrees

• 60 degrees and 70 degrees

• 40 degrees and 90 degrees

What does the Exterior Angle Theorem state?

• The exterior angle is equal to the sum of the two remote interior angles.

• The exterior angle is equal to the sum of the adjacent interior angles.

• The exterior angle is equal to the sum of all interior angles.

• The exterior angle is equal to the sum of the opposite interior angles.

In a triangle, if the exterior angle is 105 degrees and one remote interior angle is 45 degrees, what is the measure of the other remote interior angle?

• 80 degrees

• 70 degrees

• 60 degrees

• 50 degrees

If the exterior angle of a triangle is 80 degrees and one remote interior angle is 30 degrees, what is the measure of the other remote interior angle?

• 70 degrees

• 60 degrees

• 50 degrees

• 40 degrees

In a triangle, if one interior angle is 100 degrees and another is 30 degrees, what is the measure of the third interior angle?

• 70 degrees

• 60 degrees

• 50 degrees

• 40 degrees

If the exterior angle of a triangle is 80 degrees, what is the measure of the adjacent interior angle?

• 100 degrees

• 110 degrees

• 120 degrees

• 90 degrees