Exploring Triangle Sum Theorem and Exterior Angles

The video tutorial covers the triangle sum theorem, which states that the sum of the angles in a triangle is 180 degrees. It provides proofs using different types of triangles and examples to find missing angles. The exterior angle theorem is also introduced, explaining that an exterior angle equals the sum of the two remote interior angles. The video includes examples and problem-solving strategies using these theorems, along with corollaries related to right and obtuse angles in triangles.

What does the Triangle Sum Theorem state?

• The sum of the measures of the angles of a triangle is 270 degrees.

• The sum of the measures of the angles of a triangle is 360 degrees.

• The sum of the measures of the angles of a triangle is 180 degrees.

• The sum of the measures of the angles of a triangle is 90 degrees.

If two angles of a triangle are 50 degrees and 60 degrees, what is the measure of the third angle?

• 100 degrees

• 80 degrees

• 70 degrees

• 90 degrees

What is the measure of angle X if the other two angles in the triangle are 70 degrees and 40 degrees?

• 60 degrees

• 90 degrees

• 70 degrees

• 80 degrees

Which theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles?

• Triangle Sum Theorem

• Exterior Angle Theorem

• Pythagorean Theorem

• Vertical Angles Theorem

If an 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?

• 80 degrees

• 70 degrees

• 90 degrees

• 60 degrees

What is the measure of angle ACD if angle A is 40 degrees and angle B is 90 degrees?

• 140 degrees

• 130 degrees

• 100 degrees

• 120 degrees

If angle F is 4x and angle G is 78 degrees, and the exterior angle is 138 degrees, what is the value of x?

• 12

• 10

• 15

• 18

According to Corollary 4.1, what is the sum of the acute angles in a right triangle?

• 180 degrees

• 135 degrees

• 90 degrees

• 45 degrees

If a triangle has one right angle, what can be said about the other two angles?

• One is acute and one is obtuse.

• They are both obtuse.

• They are both acute.

• They are both right angles.

In a triangle, if one angle is 120 degrees, what is the nature of the other two angles?

• One is acute and one is obtuse.

• One is right and one is acute.

• Both are obtuse.

• Both are acute.