B Apply

Algebra B D → b d vector  bisects ∠ ABC . angle  Solve for x and find m ∠ ABC . bold italic m angle

27. m ∠ ABD = 5 x , m ∠ DBC = 3 x + 10 m angle
28. m ∠ ABC = 4 x − 12 , m ∠ ABD = 24 m angle
29. m ∠ ABD = 4 x − 16 , m ∠ CBD = 2 x + 6 m angle
30. m ∠ ABD = 3 x + 20 , m ∠ CBD = 6 x − 16 m angle

Algebra Find the measure of each angle in the angle pair described.

31. Think About a Plan The measure of one angle is twice the measure of its supplement.
    • How many angles are there? What is their relationship?
    • How can you use algebra, such as using the variable x, to help you?
32. The measure of one angle is 20 less than the measure of its complement.

In the diagram below, m ∠ ACB = 65 . bold italic m angle  Find each of the following.

33. m ∠ ACD m angle
34. m ∠ BCD m angle
35. m ∠ ECD m angle
36. m ∠ ACE m angle

37. Algebra ∠ RQS angle  and ∠ TQS angle  are a linear pair where m ∠ RQS = 2 x + 4 m angle  and m ∠ TQS = 6 x + 20 . m angle

    1. Solve for x.
    2. Find m ∠ RQS m angle  and m ∠ TQS . m angle
    3. Show how you can check your answer.

38. Writing In the diagram below, are ∠ 1 angle 1  and ∠ 2 angle 2  adjacent? Justify your reasoning.

    

39. Reasoning When B X → b x vector  bisects ∠ ABC , ∠ ABX ≅ ∠ CBX . angle  One student claims there is always a related equation m ∠ ABX = 1 2 m ∠ ABC . m angle  Another student claims the related equation is 2 m ∠ ABX = m ∠ ABC . 2 m angle  Who is correct? Explain.

40. Optics A beam of light and a mirror can be used to study the behavior of light. Light that strikes the mirror is reflected so that the angle of reflection and the angle of incidence are congruent. In the diagram, ∠ ABC angle  has a measure of 41.

    

    1. Name the angle of reflection and find its measure.
    2. Find m ∠ ABD . m angle
    3. Find m ∠ ABE m angle  and m ∠ DBF . m angle
41. Reasoning Describe all situations where vertical angles are also supplementary.

Table of Contents