With respect to the diagram, which relationship is false if ∠fea is supplementary to ∠hgd?

a) m∠feb + m∠hgd = 180°

b) ∠hgd≅∠feb

c) m∠hgc + m∠feb = 180°

d) ∠fea≅∠hgc

A) m∠FEB + m∠HGD = 180°

Step-by-step 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

Hence Option A is false

step-by-step explanation: