Find the measure of the angle in the diagram here, given that the two horizontal segments are parallel.

Source: NCTM Mathematics Teacher, February 2008

**Solution
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Complete a seven-sided concave polygon by drawing a perpendicular line to the two parallel lines as shown in the diagram. Note that the interior of the polygon is made up of five triangles. Hence the sum of the polygon’s seven interior angles = . The measure of the interior angle . So, the measure of the exterior angle .

**Answer**:

**Alternative solution**

Draw lines parallel to the two base lines through the vertex of each angle. Apply a series of theorems on angles formed by parallel lines and transversals such as Consecutive Interior Angles, Alternate Interior Angles, to show that the measure of .