Question

in the given figure ABCD is a quadrilateral in which angle A equal to 120 degree angle B equal to 104 degree and Angle AdC = 46degree if BC is parallel to dc and ad intersect ce at f , find measure of angle fde​

Answer 1

Answer:

given that :

ABCD is a rhombus

⇒∠BAD=∠DCB=72∘   opposite angles in a rhombus are equal 

 ∠GCF=∠DCB=72∘ vertically opposite angles 

ΔFIH is a equilateral triangle 

⇒∠HFI=60∘

⇒∠GFC=∠HFI=60∘ vertically opposite angles 

given that EC parallel to FG and FC is transversal

⇒∠GFC=∠y=60∘   ailternate interior angles 

In ΔGFC 

sum of all angles of a triangle =180∘

⇒∠x+∠GFC+∠GCF=180∘  

⇒∠x+72∘+60∘=180∘  

⇒∠x=48∘