Question

in the given figure if AB is parallel to CD and angle APQ =50 degree and
angle PRD =127 degree

find x and y​

Answer 1

Answer:

see above picture. ........

Answer 2

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

$\underline\bold\pink{Given-}$

AB || CD

Angle APQ = 50°

Angle PRD = 127°

$\underline\bold\pink{To\:find-}$

=> Measure of x and y.

$\underline\bold\pink{Proof-}$

We know that,

If lines are parallel, then their alternate interior angles are also equal.

So,

Angle APR = Angle PRD ( alternate interior angles )

y + Angle APQ = Angle PRD ( Angle APR = Angle APQ + y )

put the given values in above equation.

y + 50° = 127

y = 127° - 50°

$\huge\boxed{y\:=\:77\:°}$

___________________________

Now,

We know that,

Sum of angles which make linear pair is equal to 180°,

So,

Angle APQ + y + x = 180°

Put the given value and y = 77°.

We get,

50° + 77° + x = 180°

127° + x = 180°

x = 180° - 127°

$\huge\boxed{x\:=\:53\:°}$

_________________________

Hence, x = 53° and y = 77°.