Question

The sum of the measures of angles x and y is 127 degree. If the measure of `anglex` is 34 more than half the measure of `angle y`, what is the measure of each angle?

Answer 1

`x=65^@,y=62^@`

Explanation:

`"we can write the following equations from the statements"`

`x+y=127to(1)`

`x=1/2y+34to(2)`

`"substitute " (2)" into " (1)`

`rArr1/2y+34+y=127`

`rArr3/2y+34=127`

`"subtract 34 from both sides"`

`3/2ycancel(+34)cancel(-34)=127-34`

`rArr3/2y=93`

`rArry=93/(3/2)=93xx2/3=62`

`"substitute this value into " (1)" and solve for x"`

`x+62=127rArrx=65`

`rArrx=65^@" and " y=62^@`

`color(blue)"As a check " 62+65=127`

Answer 2

`x=65,y=62`

Explanation:

Let the measure of angle x be `x` and angle y be `y`.

We are given two pieces of information:
`x+y=127` .........(1)
`x=y/2+34` .........(2)

Substituting (2) into (1) gives
`y/2+34+y=127`
`y=62`

Substituting `y=62` into (1) gives
`x+62=127`
`x=65`

Therefore `x=65,y=62`