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# Two angles are supplementary. One angle has a measure that is five less than four times the other . What is the measure of the larger angle?

$( A ) 135^{\circ} \\ ( B ) 155^{\circ} \\ ( C ) 145^{\circ} \\( D ) 143^{\circ}$

• Two angles are supplementary if the sum of the angles is $180^\circ$
Let $a$ and $b$ be the two angles.
Then $a + b = 180$ -- ( 1 )
Also $a = 4b - 5$
Substituting above value of $a$ in ( 1 ),
$4b - 5 + b = 180$
$5b = 180 + 5 = 185$
$b = \frac{185}{5} = 37^\circ$
Hence $a = 180 - b = 180 - 37 = 143^\circ$