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Home > CCG > Chapter 6 > Lesson 6.1.5 > Problem 6-46

6-46.

Copy the diagram below onto your paper. If and , find the measures of each labeled angle. Explain how you find each angle, citing definitions and theorems from your toolkit that support your steps. Remember that you can find the angles in any order, depending on the angle relationships you use.
Two horizontal parallel lines with a triangle drawn between them. The vertex is at the top parallel line. The angles about the top parallel line and the top triangle vertex: outside triangle, left, d, Top vertex, c, outside triangle, right, e. The angles about the bottom parallel line and the two base triangle angles are:outside triangle, left, f, Inside triangle, left vertex, a, inside triangle, right vertex, b, and outside triangle, right, g.

You can find the angles in any order.

Since and  are adjacent supplementary angles (linear pair), then we can solve this algebraically.

and are another linear pair.
They also are supplementary.

If parallel lines are cut by a transversal, then alternate interior angles are congruent.

Using the Triangle Angle Sum theorem:

, , , , , ,