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Home > CCG > Chapter 5 > Lesson 5.2.1 > Problem 5-53

5-53.

Use the relationships found in each of the diagrams below to solve for and . Assume the diagrams are not drawn to scale. State which geometric relationships you used. Homework Help ✎

  1. diagram

    Solve for the missing angle in the triangle with and . Use the Triangle Angle Sum Theorem to solve for the missing angle.

    and the angle are supplementary angles, because they form a linear pair.

    The angle and the angle across from it are vertical angles and vertical angles are congruent.

    Using the Triangle Angle Sum Theorem and the triangle on the right, so

  1. diagram

    ,

  1. diagram

    Find the measures of any angles that may relate to the unknown angles by using the angles given.

  1. triangle

    This is a special right triangle. Try drawing it to scale and then solve for and .