Question

EFGH is a rhoumbus if angle EGH=40° then angle EHF=?​

Answer 1

Here, EFGH is rhombus and EG is diagonal.

In △EFG,

⇒ EF=FG [ Sides of rhombus are equal ]

⇒ ∠2=∠4 [ Angles opposite to equal sides are equal ] ----- ( 1 )

Now, EH∥FG and EG is transversal. [ Opposite sides of rhombus are parallel ]

⇒ ∠1=∠4 [ Alternate angles ] ----- ( 2 )

From ( 1 ) and ( 2 ),

⇒ ∠1=∠2

⇒ EG bisects ∠E

Now, EF∥GH and EG is transversal.

⇒ ∠2=∠3 [ Alternate angles ] ----- ( 3 )

From ( 1 ) and ( 3 )

⇒ ∠4=∠3

⇒ EG bisects ∠G

Hence, EG bisects ∠E and ∠G

Hope it helps