Standardized Test Prep

SAT/ACT

43. The measure of one angle of a triangle is 115. The other two angles are congruent. What is the measure of each of the congruent angles?
    1. 32.5
    2. 57.5
    3. 65
    4. 115
44. The center of the circle below is at the origin. What is the approximate length of its diameter?
    6. 2
    7. 2.8
    8. 5.6
    9. 8

       

45. One statement in a proof is “ ∠ 1 angle 1  and ∠ 2 angle 2  are supplementary angles.” The next statement is “ m ∠ 1 + m ∠ 2 = 180 . m angle , 1 plus , m angle . 2 equals 180 . ” Which is the best justification for the second statement based on the first statement?
    1. The sum of the measures of two right angles is 180.
    2. Angles that form a linear pair are supplementary.
    3. Definition of supplementary angles
    4. The measure of a straight angle is 180.

Extended Response

46. Δ ABC cap delta  is an obtuse triangle with m ∠ A = 21 m angle , eh equals 21  and ∠ C angle c  is acute.

    1. What is m ∠ B + m ∠ C ? m angle , b plus , m angle c question mark  Explain.
    2. What is the range of whole numbers for m ∠ C ? m angle c question mark  Explain.
    3. What is the range of whole numbers for m ∠ B ? m angle b question mark  Explain.

Mixed Review

See Lesson 3-4.

Use the diagram below for Exercises 47 and 48.

47. If ∠ 1 angle 1  and ∠ 2 angle 2  are supplementary, what can you conclude about lines a and c? Justify your answer.
48. If a | | c , eh vertical line vertical line c comma  what can you conclude about lines a and b? Justify your answer.

See Lesson 1-5.

49. ∠ ABC angle  and ∠ CBD angle  form a linear pair. If m ∠ ABC = 3 x + 20 m angle  and m ∠ CBD = x + 32 , m angle  find the value of x.
50. ∠ 1 angle 1  and ∠ 2 angle 2  are supplementary. If ∠ 1 ≅ ∠ 2 , angle 1 approximately equal to angle 2 comma  find m ∠ 1 m angle 1  and m ∠ 2 . m angle 2 .  Explain.

Get Ready! To prepare for Lesson 3-6, do Exercises 51–53.

See Lesson 1-6.

Use a straightedge to draw each figure. Then use a straightedge and compass to construct a figure congruent to it.

51. a segment
52. an obtuse angle
53. an acute angle

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