Two complementary angles differ by 12° then the angles are A) 53°, 41° B) 51°, 39° C) 54°, 42° D) 52°, 40° Ο Α OB О

Question

Two complementary angles differ by 12° then the
angles are
A) 53°, 41° B) 51°, 39° C) 54°, 42° D) 52°, 40°
Ο Α
OB
Ос
OD​

in progress 0
Quinn 2 weeks 2021-09-10T20:41:34+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-10T20:42:36+00:00
    • Option (B) 51°, 39° is correct.

    Given :–

    • Two complementary angles differ by 12°.

    To Find :–

    • The angles.

    Solution :–

    Let,

    The first angle be x.

    We know that,

    Sum of two complementary angles = 90°.

    That means,

    The second angle be 90° – x.

    According to the condition,

    Difference between both angles is 12°.

    I.e.,

    • First angle – Second angle = 12°

    So,

     \longmapsto x - (90 \degree - x) = 12 \degree

    Now, open the bracket.

     \longmapsto x - 90 \degree + x = 12 \degree

     \longmapsto x + x - 90 \degree = 12 \degree

     \longmapsto2x - 90 \degree = 12 \degree

     \longmapsto2x = 12 \degree + 90 \degree

     \longmapsto2x = 102 \degree

     \longmapsto x = \cancel \dfrac{102 \degree}{2}

     \longmapsto x = 51 \degree

    So,

    The first angle = x = 51°

    The second angle = 90° – x = 90° – 51° = 39°

    Hence,

    The first angle is 51° and the second angle is 39°.

    So, the option (B) is correct.

    Verification :–

    Substitute the both angles in equation (1),

      \longmapsto x - (90 \degree - x) = 12 \degree

    Here the values are,

    • x = 51°
    • 90° – x = 39°
    • Difference between both the angles = 12°

      \longmapsto 51 \degree - 39 \degree = 12 \degree

     \longmapsto12 \degree = 12 \degree

    Hence Verified !!

    0
    2021-09-10T20:42:48+00:00

    Answer:

    I think O B is the answer of questions

    Step-by-step explanation:

    the sum of complementary angles =90°

    90-51 gives us 39° and difference between the both is 12°

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