Two angles are complementary. The sum of the measure of the first angle and half the second angle is 74. What are the measures of the angles?
From the question, write the following system of equations:
The first equation is true since the two angles are complementary. The second can be written by the other description in the question.
Add the two (linear combination):
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Let the first angle be ( x ) degrees and the second angle be ( y ) degrees.
Since the angles are complementary, we have:
[ x + y = 90^\circ ]
Given that the sum of the measure of the first angle and half the second angle is 74, we have:
[ x + \frac{1}{2}y = 74 ]
Now, we can solve these two equations simultaneously to find the values of ( x ) and ( y ):
From the first equation, we can express ( x ) as:
[ x = 90 - y ]
Substitute this expression for ( x ) into the second equation:
[ 90 - y + \frac{1}{2}y = 74 ]
[ 90 + \frac{1}{2}y - y = 74 ]
[ 90 - \frac{1}{2}y = 74 ]
[ - \frac{1}{2}y = 74 - 90 ]
[ - \frac{1}{2}y = -16 ]
[ y = -16 \times (-2) ]
[ y = 32 ]
Now, substitute the value of ( y ) back into the first equation to find ( x ):
[ x = 90 - 32 ]
[ x = 58 ]
Therefore, the measures of the angles are ( x = 58^\circ ) and ( y = 32^\circ ).
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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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