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Math Grade 6-8 Answer Key

Angle Relationships: Complementary and Supplementary

Finding missing angles that add to 90 degrees or 180 degrees

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Angle Relationships: Complementary and Supplementary

Finding missing angles that add to 90 degrees or 180 degrees

Math - Grade 6-8

Instructions: Read each problem carefully. Use the definitions of complementary and supplementary angles to find each answer. Show your work in the space provided.
  1. 1

    Two angles are complementary. One angle measures 35 degrees. What is the measure of the other angle?

    Complementary angles have a sum of 90 degrees.

    The other angle measures 55 degrees because complementary angles add to 90 degrees, and 90 - 35 = 55.
  2. 2

    Two angles are supplementary. One angle measures 112 degrees. What is the measure of the other angle?

    The other angle measures 68 degrees because supplementary angles add to 180 degrees, and 180 - 112 = 68.
  3. 3

    Angles A and B are complementary. Angle A measures 27 degrees. Write and solve an equation to find the measure of angle B.

    Let B represent the unknown angle measure.

    The equation is 27 + B = 90. Subtracting 27 from both sides gives B = 63, so angle B measures 63 degrees.
  4. 4

    Angles C and D are supplementary. Angle C measures 49 degrees. Write and solve an equation to find the measure of angle D.

    The equation is 49 + D = 180. Subtracting 49 from both sides gives D = 131, so angle D measures 131 degrees.
  5. 5

    An angle measures 64 degrees. Is its complement or its supplement larger? Find both angle measures and explain.

    Find both missing angles, then compare the results.

    The complement is 26 degrees because 90 - 64 = 26. The supplement is 116 degrees because 180 - 64 = 116. The supplement is larger.
  6. 6

    An angle and its complement have equal measures. What is the measure of each angle?

    Each angle measures 45 degrees because complementary angles add to 90 degrees, and 90 divided by 2 is 45.
  7. 7

    An angle and its supplement have equal measures. What is the measure of each angle?

    If the two angles are equal, split the total sum into two equal parts.

    Each angle measures 90 degrees because supplementary angles add to 180 degrees, and 180 divided by 2 is 90.
  8. 8

    Two angles form a straight line. One angle measures 73 degrees. What is the measure of the other angle, and what relationship do the angles have?

    The other angle measures 107 degrees because angles that form a straight line add to 180 degrees. The angles are supplementary.
  9. 9

    The measure of an angle is x degrees. Its complement measures 2x degrees. Find the value of x and the measure of each angle.

    Set up an equation using a sum of 90 degrees.

    Since the angles are complementary, x + 2x = 90. This gives 3x = 90, so x = 30. The angles measure 30 degrees and 60 degrees.
  10. 10

    The measure of an angle is x degrees. Its supplement measures x + 40 degrees. Find the value of x and the measure of each angle.

    Since the angles are supplementary, x + x + 40 = 180. This gives 2x + 40 = 180, so 2x = 140 and x = 70. The angles measure 70 degrees and 110 degrees.
  11. 11

    Decide whether angles measuring 38 degrees and 52 degrees are complementary, supplementary, or neither. Explain your answer.

    Add the two angle measures first.

    The angles are complementary because 38 + 52 = 90, and complementary angles have a sum of 90 degrees.
  12. 12

    Decide whether angles measuring 95 degrees and 85 degrees are complementary, supplementary, or neither. Explain your answer.

    The angles are supplementary because 95 + 85 = 180, and supplementary angles have a sum of 180 degrees.
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