○=> Correct option :
[tex] \color{plum} \tt \bold{(a) \: y = 80, x = 100}[/tex]
○=> Steps to derive correct option :
Sum of all angles in a quadrilateral = 360°
Given :
▪︎Measure of angle U in quadrilateral RSTU = 80°
We know that corresponding angles in a quadrilateral are equal.
Which means :
▪︎Angle U = Angle y
Thus, the measure of angle y = 80°
Angle T = angle x (corresponding angles of a quadrilateral are equal)
Let us name angle T and angle x together as 2x.
Which means :
[tex] = \tt 80 + 80 + 2x = 360[/tex]
[tex] = \tt160 + 2x = 360[/tex]
[tex] \tt \: \: \: \: = 2x = 360 - 160 \: \ \\ = \tt120[/tex]
[tex] = \tt \: x = \frac{200}{2} [/tex]
[tex] \hookrightarrow \color{plum}\tt angle \: x = 100°[/tex]
Thus, the measure of angle x = 100°
Therefore, the correct option is (a) y = 80, x = 100
