Exploring the Triangle Sum Theorem

Mr. Dallas explains the triangle sum theorem, which states that the sum of the interior angles of a triangle is always 180 degrees. He provides several example problems, starting with basic calculations and progressing to more complex scenarios involving multiple triangles and shared vertices. The video emphasizes the importance of understanding linear pairs and vertical angles in solving these problems.

What does the Triangle Sum Theorem state?

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

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

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

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

Which of the following is true about the Triangle Sum Theorem?

• It only applies to right triangles.

• It only applies to isosceles triangles.

• It applies to all triangles regardless of their type.

• It only applies to equilateral triangles.

If a triangle has angles of 60 degrees and 85 degrees, what is the measure of the third angle?

• 65 degrees

• 35 degrees

• 55 degrees

• 45 degrees

What is the measure of the missing angle if the given angles are 92 degrees and 32 degrees?

• 56 degrees

• 58 degrees

• 60 degrees

• 62 degrees

In a triangle, if one angle is 106 degrees and another is 47 degrees, what is the measure of the third angle?

• 27 degrees

• 37 degrees

• 57 degrees

• 47 degrees

What is the measure of angle 2 if it forms a vertical angle with a 27-degree angle?

• 27 degrees

• 57 degrees

• 37 degrees

• 47 degrees

If two angles in a triangle are 58 degrees and 27 degrees, what is the measure of the third angle?

• 85 degrees

• 95 degrees

• 105 degrees

• 115 degrees

In a complex problem involving multiple triangles, what is the measure of angle 1 if the other two angles are 105 degrees and 75 degrees?

• 115 degrees

• 100 degrees

• 105 degrees

• 110 degrees

What is the measure of angle 3 if it forms a vertical angle with a 72-degree angle and another angle in the triangle is 45 degrees?

• 83 degrees

• 63 degrees

• 73 degrees

• 93 degrees

If angle 4 is part of a linear pair with a 72-degree angle, what is its measure?

• 128 degrees

• 98 degrees

• 108 degrees

• 118 degrees