Question

Find the values of x and y

Answer 1

Ok so 80 and 4x-y form a straight angle.
80+(4x-y)=180
4x-y=100

(4x-y) and (x+2y+10) also form a straight angle, but we know that 4x-y=100
100+x+2y+10=180
x+2y+110=180
x+2y=70

Now we have a system of equation
4x-y=100
x+2y=70

Solve the first equation for y
-y=-4x+100
y=4x-100

Substitute y
x+2(4x-100)=70
x+8x-200=70
9x=270
x=30

Now plug in the known x value
30+2y=70
2y=40
y=20

Final answer: x=30, y=20

Answer 2

The values of
`x=30^(\circ)` and
`y=20^(\circ)`.

Explanation:

A Linear pair is a pair of adjacent angles formed when two lines intersect.

In the given figure,
`80^(\circ)` and
`4x-y` ,
`4x-y` and
`x+2y+10^(\circ)` form a linear pair.

By linear pairs theorem, we have

`80^(\circ)+4x-y=180^(\circ)`

`4x-y+x+2y+10^(\circ)=180^(\circ)`

On solving we get,

`4x-y=100^(\circ)` ....(1)

`5x+y=170^(\circ)` .....(2)

Now, to solve equation (1) and (2) by simultaneously; we get
`x=30^(\circ)`

putting the value of x in equation 1 we get,

`4x-y=100^(\circ)`

`4\cdot 30^(\circ)-y=100^(\circ)`

`120^(\circ)-y=100^(\circ)`

On simplify we have,
`y=20^(\circ)`

Therefore, the values of x and y are:
`30^(\circ)` and
`20^(\circ)`