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°.
