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?

Answer 1

#58˚,32˚#

Call the measures of the angles #mangle1# and #mangle2#.

From the question, write the following system of equations:

#{(mangle1+mangle2=90),(mangle1+1/2mangle2=74):}#

The first equation is true since the two angles are complementary. The second can be written by the other description in the question.

Multiply the entire second equation by #-1#.
#{(mangle1+mangle2=90),(-mangle1-1/2mangle2=-74):}#

Add the two (linear combination):

#color(white)(xxxx)1/2mangle2=16# #color(white)(xxxx)color(red)(mangle2=32#
Plug this into the first equation to find #mangle1#.
#color(white)(xxxx)mangle1+32=90# #color(white)(xxxx)color(red)(mangle1=58#
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Answer 2

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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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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