Exploring Triangle Angle Sum Theorems

Nyssa Thomas introduces the triangle angle sum theorem, explaining that the sum of a triangle's angles is always 180 degrees. She demonstrates solving a problem involving a right triangle. The video also covers the triangle exterior angle theorem, showing how the exterior angle equals the sum of the two remote interior angles. Nyssa solves a problem using this theorem and encourages students to practice with additional problems.

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

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

If angle A is 50 degrees and angle B is 60 degrees, what is the measure of angle C in a triangle?

• 100 degrees

• 90 degrees

• 80 degrees

• 70 degrees

In a right triangle, if one of the angles is 90 degrees and another angle is 30 degrees, what is the measure of the third angle?

• 120 degrees

• 90 degrees

• 60 degrees

• 30 degrees

Given a right triangle with angles 90 degrees, 8x + 2 degrees, and 9x + 3 degrees, what is the value of x?

• 4

• 7

• 5

• 6

What is the Triangle Exterior Angle Theorem?

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

• The exterior angle is equal to the difference 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 all three interior angles.

If the exterior angle of a triangle is 120 degrees and one of the remote interior angles is 50 degrees, what is the measure of the other remote interior angle?

• 90 degrees

• 60 degrees

• 70 degrees

• 80 degrees

In a triangle, if the exterior angle is 8 + 6x degrees and the remote interior angles are 30 degrees and 4x + 2 degrees, what is the value of x?

• 10

• 13

• 11

• 12

If the exterior angle of a triangle is 100 degrees and one of the remote interior angles is 40 degrees, what is the measure of the other remote interior angle?

• 50 degrees

• 80 degrees

• 60 degrees

• 70 degrees

What is the measure of angle U if the other two angles in the triangle are 45 degrees and 55 degrees?

• 70 degrees

• 80 degrees

• 90 degrees

• 100 degrees

If the value of x in a triangle is 10 and one of the angles is 3x degrees, what is the measure of that angle?

• 50 degrees

• 20 degrees

• 30 degrees

• 40 degrees