Find the values of the variables and the measures of the angles.

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32. 

33. Proof Prove the Triangle Exterior Angle Theorem (Theorem 3-11).

    The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

    Given: ∠ 1 angle 1  is an exterior angle of the triangle.

    Prove: m ∠ 1 = m ∠ 2 + m ∠ 3 m angle , 1 equals , m angle , 2 plus , m angle 3

    

34. Reasoning Two angles of a triangle measure 64 and 48. What is the measure of the largest exterior angle of the triangle? Explain.
35. Algebra A right triangle has exterior angles at each of its acute angles with measures in the ratio 13 : 14. Find the measures of the two acute angles of the right triangle.

C Challenge

Probability In Exercises 36–40, you know only the given information about the measures of the angles of a triangle. Find the probability that the triangle is equiangular.

36. Each is a multiple of 30.
37. Each is a multiple of 20.
38. Each is a multiple of 60.
39. Each is a multiple of 12.
40. One angle is obtuse.
41. In the figure below, C D ¯ ⊥ A B ¯ c d bar , up tack , eh b bar  and C D ¯ c d bar  bisects ∠ ACB . angle  Find m ∠ DBF . m angle

    

42. If the remote interior angles of an exterior angle of a triangle are congruent, what can you conclude about the bisector of the exterior angle? Justify your answer.

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