MathematicsIf the difference of two complementary angles is 10, then what is the measure of the smaller angle?

If the difference of two complementary angles is 10, then what is the measure of the smaller angle?


  1. A
    40∘
  2. B
    50∘
  3. C
    45∘
  4. D
    35∘  

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    Solution:

    Given,
    Difference of two complementary angles = 10
    Let first angle =x.
    Then its complementary angle =90°-x.
    Also, given that the difference of the complementary angles is 10o.
    Then,
    x-(90°-x)=10° ⟹x-90°+x=10° ⟹2x=10°+90°=100° ⟹x=50°.
    Second angle = 90° - 50°=40°.
    Hence, the smaller angle =40∘.
    Therefore, option 1 is correct.
     
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