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Questions  >>  Olympiad-Math  >>  Class 7  >>  Lines and Angles
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Q)

The difference in the measures of two complementary angles is $12^{\circ}$. Find the measures of the angles.


$( A ) 32^{\circ},58^{\circ} \\ ( B ) 39^{\circ},51^{\circ} \\ ( C ) 31^{\circ},59^{\circ} \\ ( D ) None\; of\; these$

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A)
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  • Two angles are complementary when their sum adds to $90^{\circ}$
Let $x$ be one angle. Then $90-x$ is another angle.
So $x - (90-x) = 12$
$x - 90 +x = 12 $
$ 2x = 12 + 90 = 102 $
$ x = \frac{102}{2} = 51 $
Hence angles are 51 and 39 ( 90 - 51 ).
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