In the right-hand isosceles triangle, the two bottom angles are equal.
The three angles add up to 180°, so:
[tex]50+2(2y+64)=180[/tex]
⇒[tex]50+4y+128=180[/tex]
⇒[tex]4y+178=180[/tex]
⇒[tex]4y=2[/tex]
⇒[tex]y=\frac{1}{2}[/tex]
The angle [tex]2y+64[/tex] comes out as [tex]2(\frac{1}{2})+64=1+64=65[/tex]
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:
[tex]125+2(45-\frac{x}{4})=180[/tex]
⇒[tex]125+90-\frac{x}{2}=180[/tex]
⇒[tex]215-\frac{x}{2}=180[/tex]
⇒[tex]215-180=\frac{x}{2}[/tex]
⇒[tex]\frac{x}{2}=35[/tex]
⇒[tex]x=70[/tex]
So [tex]x=70[/tex] and [tex]y=\frac{1}{2}[/tex]
