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

Question

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

Answer 1

Toolbox:

• 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 $\alpha = 180 - \beta = 180 - 98 = 82^\circ$