# The supplement of an angle has a measure that is three times the angle. What is the measure of the angle and measure of the supplement?

The angle equals

Since the supplement is three times the angle, we can say

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Let ( x ) be the measure of the angle. Then, the supplement of the angle has a measure of ( 180^\circ - x ). According to the given statement, the supplement is three times the angle. Thus:

[ 180^\circ - x = 3x ]

Solve for ( x ) to find the measure of the angle.

[ 180^\circ - x = 3x ] [ 180^\circ = 4x ] [ x = \frac{180^\circ}{4} ] [ x = 45^\circ ]

So, the measure of the angle is ( 45^\circ ).

To find the measure of the supplement:

[ 180^\circ - x = 180^\circ - 45^\circ = 135^\circ ]

Thus, the measure of the supplement is ( 135^\circ ).

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