Exploring Triangle Sum and Exterior Angles

The video tutorial covers two main topics: the Triangle Sum Theorem and the Exterior Angle Theorem. The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. The Exterior Angle Theorem explains that an exterior angle of a triangle is equal to the sum of the two remote interior angles. The tutorial includes examples and problem-solving exercises to illustrate these concepts.

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

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

If a triangle has angles measuring 58 degrees and 47 degrees, what is the measure of the third angle?

• 105 degrees

• 95 degrees

• 85 degrees

• 75 degrees

In a right triangle, if one of the angles is 31 degrees and the other is represented by the expression 3x - 1, what is the value of x?

• 25

• 15

• 20

• 10

What is an exterior angle of a triangle?

• An angle inside the triangle

• An angle formed by extending one side of the triangle

• An angle that is always 90 degrees

• An angle that is always 180 degrees

Which angles are considered remote interior angles in relation to an exterior angle?

• The angles adjacent to the exterior angle

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

• The angles outside the triangle

• The angles inside the triangle that are not adjacent to the exterior angle

If an exterior angle of a triangle measures 55 degrees and one of the remote interior angles measures 34 degrees, what is the measure of the other remote interior angle?

• 41 degrees

• 31 degrees

• 51 degrees

• 21 degrees

In a triangle, if the exterior angle is 100 degrees and one of the remote interior angles is 51 degrees, what is the measure of the other remote interior angle?

• 29 degrees

• 49 degrees

• 23 degrees

• 33 degrees

If two triangles share a common vertex and one of the angles at that vertex is 80 degrees, what is the measure of the angle directly opposite to it?

• 40 degrees

• 60 degrees

• 80 degrees

• 100 degrees

In a complex figure with overlapping triangles, if one of the angles in the smaller triangle is 50 degrees and another is 25 degrees, what is the measure of the third angle?

• 55 degrees

• 105 degrees

• 75 degrees

• 65 degrees

If a triangle has angles measuring 57 degrees and 43 degrees, what is the measure of the third angle?

• 70 degrees

• 80 degrees

• 90 degrees

• 100 degrees