Angle Sum Theorem (Triangle interior and exterior)

Front

What is the Angle Sum Theorem for triangles?

Back

The Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Front

If one angle of a triangle measures 90 degrees and another measures 40 degrees, what is the measure of the third angle?

Back

The third angle measures 50 degrees (180 - 90 - 40 = 50).

Front

What is the Exterior Angle Theorem?

Back

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.

Front

If angle A is 30 degrees and angle B is 50 degrees, what is the measure of the exterior angle C?

Back

The exterior angle C measures 80 degrees (30 + 50 = 80).

Front

What is the relationship between the interior angles and the exterior angles of a triangle?

Back

The sum of the measures of the interior angles is 180 degrees, while each exterior angle is equal to the sum of the two opposite interior angles.

Front

How do you find a missing angle in a triangle?

Back

To find a missing angle, subtract the sum of the known angles from 180 degrees.

Front

What is the measure of each angle in an equilateral triangle?

Back

Each angle in an equilateral triangle measures 60 degrees.

Front

If angle D is an exterior angle and measures 120 degrees, what are the measures of the two opposite interior angles?

Back

The two opposite interior angles must sum to 120 degrees.

Front

What is the formula to calculate the sum of the interior angles of a polygon?

Back

The sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees.

Front

In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees, what are the measures of the other two angles?

Back

Let the smaller angle be x. Then the angles are x, 2x, and 30. Solving gives x = 10 degrees and 2x = 20 degrees.