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anonymous

  • one year ago

The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle. 18° 36° 54° 58°

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  1. mathstudent55
    • one year ago
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    Angle: x Complement: 90 - x

  2. mathstudent55
    • one year ago
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    Sum of the complements: x + 90 - x = 90

  3. anonymous
    • one year ago
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    2x??

  4. mathstudent55
    • one year ago
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    Difference of their measures: x - (90 - x)

  5. mathstudent55
    • one year ago
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    90 exceeds x - (90 - x) by 72 That means: 90 - [x - (90 - x)] = 72

  6. mathstudent55
    • one year ago
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    Solve for x.

  7. anonymous
    • one year ago
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    ....

  8. anonymous
    • one year ago
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    i distribute the negitive?

  9. mathstudent55
    • one year ago
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    If x is more than 45, then subtract x from 90

  10. anonymous
    • one year ago
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    so it would be a

  11. anonymous
    • one year ago
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    A

  12. mathstudent55
    • one year ago
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    90 - [x - (90 - x)] = 72 90 - [x - 90 + x] = 72 90 - [2x - 90] = 72 90 - 2x + 90 = 72 -2x + 180 = 72 -2x = -108 x = 54 The measure of one of the angles is 54. Since complementary angles add to 90, the other angle is 90 - x. 90 - 54 = 36 Since they ask fot eh measure of the smaller angle, the answer is 36.

  13. anonymous
    • one year ago
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    thank you man that much simpler

  14. mathstudent55
    • one year ago
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    ^the last sentence above should read: Since they ask for the measure of the smaller angle, the answer is 36.

  15. mathstudent55
    • one year ago
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    You're welcome.

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