Triangle Sum Theorem and Exterior Angle Theorem

The video tutorial covers the basics of triangles, including their sides, vertices, and angles. It explains the triangle sum theorem, which states that the sum of a triangle's interior angles is 180 degrees, and demonstrates how to apply this theorem to find missing angles. The tutorial also introduces the exterior angle theorem, showing that an exterior angle equals the sum of the two remote interior angles. Exercises are provided to reinforce these concepts, including using ratios to find angle measures. The lesson concludes with a summary of key points.

What is a triangle by definition?

• A polygon with four sides

• A polygon with three sides and four vertices

• A closed polygon with three sides

• A shape with three vertices and four angles

According to the Triangle Sum Theorem, what is the sum of the interior angles of a triangle?

• 180 degrees

• 270 degrees

• 360 degrees

• 90 degrees

If a triangle has angles measuring 90 degrees, 24 degrees, and x degrees, what is the value of x?

• 76 degrees

• 66 degrees

• 86 degrees

• 96 degrees

Can angles measuring 33 degrees, 44 degrees, and 93 degrees form a triangle?

• Yes, because they add up to 170 degrees

• No, because they add up to 170 degrees

• No, because they add up to 180 degrees

• Yes, because they add up to 180 degrees

If the angles of a triangle are in the ratio 1:2:6, what is the measure of the largest angle?

• 40 degrees

• 20 degrees

• 60 degrees

• 120 degrees

What does the Exterior Angle Theorem state?

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

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

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

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

If an exterior angle of a triangle is 147 degrees, what is the sum of its two remote interior angles?

• 147 degrees

• 120 degrees

• 90 degrees

• 180 degrees