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

Two angles are supplementary. One angle is 212 degrees less than three times the other .find the measure of the angles


$( A ) None \;of \;these \\ ( B ) 93^{\circ},87^{\circ} \\ ( C ) 100^{\circ},80^{\circ} \\( D ) 98^{\circ},82^{\circ} $

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A)
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  • Two angles are supplementary if the sum of the angles is $180^\circ$
Let $\alpha$ and $\beta$ be the two angles.
Then $\alpha + \beta = 180$ -- ( 1 )
Also $\alpha = 3 \beta - 212$
Substituting for $\alpha$ from above in ( 1 ), we get
$3\beta - 212 + \beta = 180$
$4\beta = 180 + 212 = 392$
Hence $\beta = \frac{392}{4} = 98^\circ$
Hence $\alpha = 180 - \beta = 180 - 98 = 82^\circ$
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