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

Answer 1

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

The first angle will be expressed as #x#. Since the second angle is #120# degrees greater than the first, it will be expressed as #(x + 120)#. Because they're supplementary, they'll add up to #180#:
#x + (x + 120) = 180#

Combine like terms.

#2x + 120 = 180#

Subtract 120 from both sides.

#2x = 60#
Divide by 2 to isolate for #x#.
#x = 30#

Plug your data back in:

30 + (30 + 120) = 180

First angle: 30 degrees Second angle: 150 degrees

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Answer 2

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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