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After solving for in each of the diagrams in problem 8-6, Jerome thinks he sees a pattern. He notices that the measure of an exterior angle of a triangle is related to two of the angles of a triangle.  

  1. Do you see a pattern? To help find a pattern, study the results of problem 8-6.

    Pick examples of angles that could realistically be placed in for and (remote interior angles) in the triangle above.
    For example, and calculate the value for (the exterior angle) using the work you did in problem 8-6.
    Is there a connection between and (remote exterior angles) and (exterior angle)?

    If you picked other angles for and (remote interior angles) would your conjecture still work?

  1. Triangle with bottom side extending to the left, triangle angles labeled as follows, top is a, bottom right is b, bottom left is c, linear angle with bottom left angle, labeled x, & exterior angle, top & right bottom angles also labeled remote interior angles.In the example at right, angles and are called remote interior angles of the given exterior angle because they are not adjacent to the exterior angle. Write a conjecture about the relationships between the remote interior and exterior angles of a triangle.

    The measure of the exterior angle is equal to the sum of the remote interior angles.

  2. Prove that the conjecture you wrote for part (b) is true for all triangles. Your proof can be written in any form, as long as it is convincing and provides reasons for all statements.