Question

Find the values of x and y

Answer 1

Answer:

The values of $x=30^{\circ}$ and $y=20^{\circ}$.

Step-by-step 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 $20^{\circ}$

Answer 2

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