Exploring Triangle Sum and Exterior Angle Theorems

This video tutorial covers the triangle sum theorem, which states that the sum of the angles in a triangle is 180 degrees. It also explores the exterior angle theorem, which relates the exterior angle to the sum of the opposite interior angles. The tutorial includes examples and exercises to illustrate these concepts, and it incorporates algebra to solve for unknown angles. The video emphasizes understanding the relationships between angles and using logical steps to solve geometry problems.

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

• 270 degrees

• 90 degrees

• 180 degrees

• 360 degrees

According to the Exterior Angle Theorem, the measure of an exterior angle is equal to the sum of which angles?

• The two opposite exterior angles

• The two exterior angles

• The two non-adjacent interior angles

• The two adjacent interior angles

If one angle of a triangle is 24 degrees and another is 37 degrees, what is the measure of the third angle?

• 133 degrees

• 129 degrees

• 123 degrees

• 119 degrees

In a triangle, if two interior angles are 76 degrees and 52 degrees, what is the measure of the opposite exterior angle?

• 130 degrees

• 128 degrees

• 124 degrees

• 132 degrees

If a triangle has angles of 66 degrees and 84 degrees, what is the measure of the third angle?

• 60 degrees

• 30 degrees

• 40 degrees

• 50 degrees

In a triangle with angles 43 degrees and 96 degrees, what is the measure of the third angle?

• 71 degrees

• 61 degrees

• 51 degrees

• 41 degrees

If two parallel lines are cut by a transversal, what is the relationship between alternate interior angles?

• They are complementary

• They are congruent

• They are equal to 180 degrees

• They are supplementary

Solve for x: 9x + 3 + 5x - 2 + 11x - 21 = 180

• x = 7

• x = 9

• x = 6

• x = 8

If 13x - 11 + 4x + 1 = 75, what is the value of x?

• x = 3

• x = 4

• x = 5

• x = 6

In a triangle, if one angle is 54 degrees and another is 21 degrees, what is the measure of the third angle?

• 135 degrees

• 105 degrees

• 125 degrees

• 115 degrees