Exploring Triangle Angle Sum and Exterior Angle Theories

This video tutorial covers key concepts in geometry, including the triangle angle sum theorem and the exterior angle theorem. It begins with an introduction to supplementary and vertical angles, followed by a detailed explanation of the triangle angle sum theorem. The video then explores the exterior angle theorem with practical examples. It progresses to solving complex problems involving multiple triangles and using algebra to find unknown angles. Finally, it discusses the properties of isosceles triangles, providing a comprehensive understanding of these geometric principles.

What is the sum of supplementary angles?

• 180 degrees

• 45 degrees

• 90 degrees

• 360 degrees

If angle 1 is 118 degrees, what is the measure of angle 2 if they are supplementary?

• 92 degrees

• 72 degrees

• 62 degrees

• 82 degrees

What is true about vertical angles?

• They are always adjacent

• They are always supplementary

• They are always equal

• They are always complementary

In a triangle, if two angles are 27 degrees and 82 degrees, what is the measure of the third angle?

• 81 degrees

• 71 degrees

• 91 degrees

• 61 degrees

According to the exterior angle theorem, what is the measure of the exterior angle if the two non-adjacent interior angles are 70 degrees and 50 degrees?

• 110 degrees

• 120 degrees

• 130 degrees

• 140 degrees

If the exterior angle is 115 degrees and one of the non-adjacent interior angles is 50 degrees, what is the measure of the other non-adjacent interior angle?

• 85 degrees

• 55 degrees

• 65 degrees

• 75 degrees

In a triangle, if two angles are 61 degrees and 42 degrees, what is the measure of the third angle?

• 77 degrees

• 67 degrees

• 97 degrees

• 87 degrees

If angle x in a triangle is 50 degrees and the other two angles are 60 degrees and 70 degrees, what is the measure of angle x?

• 50 degrees

• 70 degrees

• 40 degrees

• 60 degrees

In an isosceles triangle, if one of the equal angles is 67 degrees, what is the measure of the third angle?

• 76 degrees

• 66 degrees

• 56 degrees

• 46 degrees

If the three angles in a triangle are represented as 8x-1, 3x+9, and 3x+4, what is the value of x?

• 11

• 10

• 13

• 12