Exploring Triangle Angle Relationships and Theorems

The video tutorial covers two main theorems in geometry: the Triangle Angle Sum Theorem and the Triangle Exterior Angle Theorem. The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. The video provides examples to illustrate this concept. The Triangle Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. Examples are provided to demonstrate this theorem as well.

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

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

If one angle of a triangle is 60 degrees and another is 45 degrees, what is the measure of the third angle?

• 75 degrees

• 85 degrees

• 95 degrees

• 105 degrees

Given a triangle with one angle measuring 30 degrees, which of the following could be the measures of the other two angles?

• 60 degrees and 90 degrees

• 50 degrees and 100 degrees

• 70 degrees and 80 degrees

• 40 degrees and 110 degrees

What does the Triangle Exterior Angle Theorem state?

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

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

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

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

In the Triangle Exterior Angle Theorem, what are the 'remote interior angles'?

• The angles that are equal to the exterior angle

• The angles adjacent to the exterior angle

• The angles that form a linear pair with the exterior angle

• The angles that are not adjacent to the exterior angle

If the exterior angle of a triangle is 124 degrees, and one of the remote interior angles is 43 degrees, what is the measure of the other remote interior angle?

• 81 degrees

• 91 degrees

• 111 degrees

• 101 degrees

Given an exterior angle of 3x - 2 degrees and remote interior angles of x and 100 degrees, what is the value of x?

• 49

• 50

• 51

• 52

If x is found to be 51 degrees in the previous problem, what is the measure of the exterior angle?

• 152 degrees

• 154 degrees

• 151 degrees

• 153 degrees

Which theorem is more useful when you do not know one of the interior angles of a triangle?

• Angle Bisector Theorem

• Triangle Exterior Angle Theorem

• Pythagorean Theorem

• Triangle Angle Sum Theorem

What is the first step in solving for x in the equation 3x - 2 = x + 100?

• Add x to both sides

• Subtract 2 from both sides

• Subtract x from both sides

• Add 2 to both sides