Question

Question : if, AB || CD, Angle APQ = 50°, Angle PRD = 127° . Find x and y.

Answer 1

$\huge\underline\mathfrak\red{Answer}$

$\huge\boxed{x\:=\:50\:°}$

$\huge\boxed{y\:=\:77\:°}$

____________________

$\huge\underline\mathfrak\red{Explanation}$

Given : AB || CD, Angle APQ = 50°, Angle PRD = 127°

To find : Measure of x and y.

Proof : Angle PQR = Angle APQ ( If lines are parallel then their alternative interior angles are also equal )

Angle PQR = x = 50°

$\huge\boxed{x\:=\:50\:°}$

_____________________

Now, Angle 1 + Angle PRD = 180° ( Linear pair )

Angle 1 + 127° = 180°

Angle 1 = 180° - 127°

Angle 1 = 53°

____________________

In ∆PQR,

By using angle sum property,

Angle 1 + x + y = 180°

53° + 50° + y = 180°

103° + y = 180°

y = 180° - 103°

$\huge\boxed{y\:=\:77\:°}$

_____________________

Therefore, x = 50° and y = 77° ( required vales )

Answer 2

Answer:

Hey mate i will help u

Refers with attachments