Question

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

Answer 1

Answer:

part D is true.

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