Find the value of x ,y and z

Dear Student,

Q u e s t i o n 7) A B ∥ E C h e n c e ∠ A B C = ∠ E C D (c o r r e s p o n d i n g a n g l e s o f p a r a l l e l s i d e s) \Rightarrow x = 45 i n △ A B C s u m o f a l l t h r e e a n g l e s o f a t r i a n g l e i s 180 \Rightarrow ∠ A B C + \lor A C B + ∠ B A C = 180 \Rightarrow x + 60 + z = 180 \Rightarrow 45 + 60 + z = 180 \Rightarrow 105 + z = 180 z = 180 - 105 z = 75 ° \sin c e z + y + 45 i s a l i n e a r p a i r h e n c e z + y + 45 = 180 75 + 45 + y = 180 y = 180 - 120 y = 60 Q u e s t i o n 6) C D ∥ E F ∠ y = 135 - - (v e r t i c a l l y o p p o s i t e a n g l e s) A l s o ∠ z + 135 = 180 (a l t e r n a t e a n g l e s) \Rightarrow ∠ z = 180 - 135 \Rightarrow ∠ z = 45 N o w ∠ x + ∠ z + 70 = 180 (C G D i s a s t r a i g h t l i n e) \Rightarrow ∠ x + 45 + 70 = 180 \Rightarrow ∠ x + 115 = 180 \Rightarrow ∠ x = 65 °

Regards,