Exploring the Triangle Angle Sum Theorem

What does the Triangle Angle Sum Theorem state?

• All three angles of a triangle add up to 180 degrees.

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

• The exterior angle of a triangle is equal to the sum of the two interior opposite angles.

• The sum of the angles in a quadrilateral is 360 degrees.

According to the Exterior Angle Theorem, what is the relationship between the interior and exterior angles?

• Interior angle equals the sum of the other two interior angles.

• Exterior angle equals the sum of all three interior angles.

• Interior plus interior equals exterior.

• Interior angle equals exterior angle.

If a triangle has angles of 24 degrees and 37 degrees, what is the measure of the third angle?

• 121 degrees

• 120 degrees

• 122 degrees

• 119 degrees

In a triangle, if one interior angle is 76 degrees and another is 52 degrees, what is the measure of the exterior angle adjacent to these two angles?

• 127 degrees

• 128 degrees

• 129 degrees

• 126 degrees

Using the Exterior Angle Theorem, if one interior angle is 79 degrees and the exterior angle is 104 degrees, what is the measure of the other interior angle?

• 25 degrees

• 23 degrees

• 26 degrees

• 24 degrees

In a triangle with angles 66 degrees and 84 degrees, what is the measure of the third angle?

• 28 degrees

• 29 degrees

• 31 degrees

• 30 degrees

If two angles form a linear pair and one angle is 84 degrees, what is the measure of the other angle?

• 94 degrees

• 97 degrees

• 96 degrees

• 95 degrees

In a triangle, if the angles are represented as 5x-2, 9x+3, and 11x-21, what is the value of x?

• 7

• 8

• 9

• 6

Using the value of x found in the previous question, what is the measure of the angle represented by 5x-2?

• 37 degrees

• 36 degrees

• 38 degrees

• 39 degrees

Using the Exterior Angle Theorem, if the interior angles are represented as 13x-11 and 4x+1, and the exterior angle is 18x-15, what is the value of x?

• 5

• 6

• 7

• 4