[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The required values are ~
[tex] \boxed{x = 75 \degree}[/tex]
and
[tex] \boxed{y = 60 \degree}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
As it's shown in the figure, the sides opposite to x and Angle 75° are equal. So the corresponding Angles are also equal to one another.
that is ~
- [tex]x = 75 \degree[/tex]
I have taken an angle and marked it as " m " in the attachment.
So, according to Angle sum property of a triangle,
- [tex]m + x + 75 \degree = 180 \degree[/tex]
- [tex]m + 75 \degree+ 75 \degree= 180 \degree[/tex]
- [tex]m + 150 \degree= 180 [/tex]
- [tex]m = 180 \degree - 150 \degree[/tex]
- [tex]m = 30 \degree[/tex]
now, it's given that the sum of Angle y and Angle m is 90°
hence,
- [tex]m + y = 90 \degree[/tex]
- [tex] 30 \degree + y = 90 \degree[/tex]
- [tex]y = 90 \degree - 30 \degree[/tex]
- [tex]y = 60 \degree[/tex]
