Question

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

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 :

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

$= \tt160 + 2x = 360$

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

$= \tt \: x = \frac{200}{2}$

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

Thus, the measure of angle x = 100°

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