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

Question

In Fig. 9.40, if AB || CD , EF || BC , &#x2220; BAC = 65&#xB0; and &#x2220; DHF = 35&#xB0;, find &#x2220; AGH.

Philoid · Accepted Answer

Given,

AB ‖ CD and,

EF ‖ BC

∠BAC = 65^o and ∠DHF = 35^o

∠BAC = ∠ACD (Alternate angles)

∠ACD = 65^o

∠DHF = ∠GHC (Vertically opposite angles)

∠GHC = 35^o

In

∠GCH + ∠GHC + ∠HGC = 180^o

65^o + 35^o + ∠HGC = 180^o

∠HGC = 80^o

∠AGH + ∠HGC = 180^o (Linear pair)

∠AGH + 80^o = 180^o

∠AGH = 100^o