Triangle Sum and Exterior Angle Theorems

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 by its sides.

Front

What is an exterior angle of a triangle?

Back

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side.

Front

State the Exterior Angle Theorem.

Back

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

Front

If one angle of a triangle is 41° and another is 59°, what is the measure of the third angle?

Back

The third angle is 80° (180° - 41° - 59°).

Front

What are remote interior angles?

Back

Remote interior angles are the two interior angles of a triangle that are not adjacent to a given exterior angle.

Front

If Angle W is an exterior angle, which angles are its remote interior angles?

Back

The remote interior angles to Angle W are the two angles inside the triangle that do not share a vertex with Angle W.

Front

How do you set up an equation to find an unknown angle in a triangle?

Back

You can set up the equation by using the Triangle Sum Theorem: x + y + z = 180°, where x, y, and z are the angles.

Front

If x + 59 + x + 51 + 84 = 180, what is x?

Back

x = 30 degrees.

Front

What is the measure of an angle if it is supplementary to a 91° angle?

Back

The measure of the angle is 89° (180° - 91°).