Question

How to solve for x and y

Answer 1

In the right-hand isosceles triangle, the two bottom angles are equal.

The three angles add up to 180°, so:

`50+2(2y+64)=180`
⇒
`50+4y+128=180`
⇒
`4y+178=180`
⇒
`4y=2`
⇒
`y=(1)/(2)`

The angle
`2y+64` comes out as
`2((1)/(2))+64=1+64=65`

The angle to the side of it is 180-65=125.

In the left-hand triangle, the angle at the left and the angle at the top are equal.

In this triangle:

`125+2(45-(x)/(4))=180`
⇒
`125+90-(x)/(2)=180`
⇒
`215-(x)/(2)=180`
⇒
`215-180=(x)/(2)`
⇒
`(x)/(2)=35`
⇒
`x=70`

So
`x=70` and
`y=(1)/(2)`