Question

In the figure below, find the value of Y and X.

Options
y = 80, x = 100
x = 80, y = 80
y = 100, x = 80
x = 100, y = 100

Answer 1

○=> Correct option :

`\color{plum} \tt \bold{(a) \: y = 80, x = 100}`

○=> 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 :

`= \tt 80 + 80 + 2x = 360`

`= \tt160 + 2x = 360`

`\tt \: \: \: \: = 2x = 360 - 160 \: \ \\ = \tt120`

`= \tt \: x = (200)/(2)`

`\hookrightarrow \color{plum}\tt angle \: x = 100°`

Thus, the measure of angle x = 100°

Therefore, the correct option is (a) y = 80, x = 100