In the following figure both ABCD and PQRS are parallelograms. Find the value of 

Asked by lalitshuklapiyus | 11th Oct, 2019, 09:23: AM

Expert Answer:

We know that in a parallelogram, opposite angles are equal
rightwards double arrow angle B A D equals angle B C D
rightwards double arrow angle B C D equals 120 degree
A l s o comma space t h e space a d j a c e n t space a n g l e s space o f space a space p a r a l l e log r a m space a r e space s u p p l e m e n t a r y
rightwards double arrow angle B C D plus angle A B C equals 180 degree
rightwards double arrow angle A B C equals 60 degree
I n space p a r a l l e log r a m space P Q R S comma
angle Q R S equals angle S P Q space... space O p p o s i t e space a n g l e s space a r e space e q u a l
rightwards double arrow angle S P Q equals 50 degree
L e t space B C space a n d space P S space i n t e r s e c t space a t space X
S o space i n space increment P X B comma
angle X P B plus angle P B X plus angle P X B equals 180 degree
rightwards double arrow angle S P Q plus angle A B C plus angle P X B equals 180 degree
rightwards double arrow 50 degree plus 60 degree plus angle P X B equals 180 degree
H e n c e comma space angle P X B equals 70 degree

Answered by Renu Varma | 11th Oct, 2019, 10:04: AM