Question

With respect to the diagram, which relationship is false if ∠FEA is supplementary to ∠HGD? m∠FEB + m∠HGD = 180° ∠HGD≅∠FEB m∠HGC + m∠FEB = 180° ∠FEA≅∠HGC Done

Answer 1

A) m∠FEB + m∠HGD = 180°

Explanation:

We are given that ∠FEA is supplementary to ∠HGD

Supplementary angles : Sum of pair of angles is 180°

⇒∠FEA +∠HGD = 180° -- 1

In figure 1 :

∠FEA +∠FEB= 180° (linear pairs) --2

Since ∠HGD is supplement to ∠FEA So, ∠FEB cannot be supplement to ∠HGD (refer figure)

So, A is false

Subtract 1 from 2

⇒∠FEA +∠FEB - ∠FEA +∠HGD = 180° - 180°

⇒∠FEB =∠HGD

So, B is true : ∠HGD≅∠FEB

Now In figure 2 :

∠HGC +∠HGD= 180° (linear pairs) --3

By part B

∠HGC +∠FEB= 180°

So, part C is true

Now subtract 3 from 1 :

⇒∠FEA +∠HGD -∠HGC-∠HGD = 180° -180°

⇒∠FEA =∠HGC

So, part D is true :∠FEA≅∠HGC

Option A is false

Answer 2

C) m∠HGC + m∠FEB = 180°