Question

In Fig. 9.40, if AB||CD, EF||BC, ∠BAC = 65° and ∠DHF = 35°, find ∠AGH.

Answer 1

In Fig. 9.40, if AB||CD, EF||BC, ∠BAC = 65° and ∠DHF = 35°,  then

∠AGH = 100°

Given,

AB||CD

EF||BC

∠ BAC = 65°

∠ DHF = 35°

To find : ∠ AGH

Proof:

Consider the attached figure while going through the following steps

∠ DHF = ∠ GHC  (vertically opposite angles are equal)

as ∠ DHF = 35°

∴ ∠ GHC = 35°

∠ BAC = ∠ ACD  (vertically opposite angles are equal)

as ∠ BAC = 65°

∴ ∠ ACD = 65°

∠ HCG = ∠ BAC = 65° (angles forming a linear pair are supplementary)

In Δ GHC

∠ GHC + ∠ HCG  + ∠ CGH  = 180°

35° + 65° + ∠ CGH  = 180°

100° + ∠ CGH  = 180°

∠ CGH  = 180° - 100°

∴ ∠ CGH = 80°

Given, AGC is a straight line.

∠ CGH + ∠ AGH = 180°

80° + ∠ AGH = 180°

∠ AGH = 180° - 80°

∴ ∠ AGH = 100°

Answer 2

Depressants help to separatetwo sulphide ores by selective prevention of froth formation by one ore and allowing the other to come into the froth. NaCN isused as a depressant in order to separatetwo sulphide ores (ZnS and PbS).