Question

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˚`

Explanation:

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`