Outside Angles :

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Using Outside Angles

You may occasionally need to use an angle outside of a triangle to find an angle inside that triangle. Because a straight line can also be described as a straight angle that measures 180°, you can find the measure of any inside angle if you know the outside angle.

For example, you have a triangle labeled EDF that sits on line segment EFG. E and the F are points on the line and also vertexes of the triangle. The D is the top vertex of the triangle and G is the furthest point on line EFG. You know two things about triangle EDF - that $\angle DEF$ is 81 degrees and the the outside angle of vertex F, $\angle DFG$ , is 148 degrees. That is enough information to find all three angles of triangle EDF.

Step 1: Subtract 148° from 180° to find the measure of $\angle EFD$

$180^\circ -148^\circ = 32^\circ$

Step 2: Find the sum of the known angles.

$81^\circ + 32^\circ = 113^\circ$

Step 3: Subtract 113° from 180° to find the unknown angle.

$180^\circ -113^\circ = 67^\circ$

Answer: The measure of $\angle EDF$ is 67°.