Triangle Sum Theorem and Exterior Angle Theorem

Front

What is the Triangle Sum Theorem?

Back

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

Front

What are the interior angles of a triangle?

Back

The interior angles of a triangle are the angles formed inside the triangle, specifically the angles at each vertex.

Front

If one angle of a triangle is 90 degrees, what can you say about the other two angles?

Back

If one angle is 90 degrees, the other two angles must sum to 90 degrees, making the triangle a right triangle.

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 remote interior angles.

Front

How do you find the measure of an exterior angle?

Back

To find the measure of an exterior angle, add the measures of the two non-adjacent (remote) interior angles.

Front

What is a remote interior angle?

Back

A remote interior angle is an interior angle of a triangle that is not adjacent to a given exterior angle.

Front

If the exterior angle of a triangle is 128 degrees, what is the relationship to the remote interior angles?

Back

The exterior angle of 128 degrees is equal to the sum of the measures of the two remote interior angles.

Front

What is the formula to find the measure of an angle in a triangle if two angles are known?

Back

If two angles are known, the measure of the third angle can be found using the formula: Third Angle = 180 - (Angle 1 + Angle 2).

Front

If two angles of a triangle are 36 degrees and 56 degrees, what is the measure of the third angle?

Back

The third angle is 180 - (36 + 56) = 88 degrees.

Front

What is the value of y if the remote interior angles are 6y - 4 and 6y, and the exterior angle is 128?

Back

Set up the equation: (6y - 4) + 6y = 128. Solving gives y = 11.