# Two angles are supplementary. The larger angle measures 120 degrees more than the smaller. What is the degree measure of each angle?

The first angle is 30 degrees. The second angle is 150 degrees. Here's why:

Combine like terms.

Subtract 120 from both sides.

Plug your data back in:

30 + (30 + 120) = 180

First angle: 30 degrees Second angle: 150 degrees

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Let the measure of the smaller angle be ( x ) degrees.

According to the problem, the larger angle is ( 120^\circ ) more than the smaller angle. Thus, the measure of the larger angle is ( x + 120^\circ ).

Since the two angles are supplementary, their sum is ( 180^\circ ).

So, we have the equation: [ x + (x + 120^\circ) = 180^\circ ]

Simplifying the equation: [ 2x + 120^\circ = 180^\circ ]

Subtracting ( 120^\circ ) from each side: [ 2x = 60^\circ ]

Dividing each side by 2: [ x = 30^\circ ]

So, the smaller angle measures ( 30^\circ ), and the larger angle measures ( 30^\circ + 120^\circ = 150^\circ ).

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