Question

in a trapezium ABCD, bisectors of angle A, B, C and D form a quadrilateral EFGH as shown. find angle HGF​

Answer 1

Given :  trapezium ABCD, bisectors of angles A, B, C and D form a quadrilateral EFGH as shown.  

To Find :  angle HGF​

Solution:

trapezium ABCD

AB || DC  

=> ∠A + ∠D = 180°  

Interior angles are supplementary. ( adds up to 180°)

AG bisector of ∠A =>  ∠DAG =  ∠A/2

DG bisector of ∠D  =>  ∠ADG = ∠D/2

in Δ ADG

∠DAG   +  ∠ADG + ∠AGD = 180°

=>  ∠A/2 +  ∠D/2 + ∠AGD = 180°

=> (∠A + ∠D)/2 + ∠AGD = 180°

=>  ( 180°)/2 + ∠AGD = 180°

=>  90° + ∠AGD = 180°

∠AGF  + ∠AGD  = 180°   ( Linear pair )

=> ∠AGF = 90°

∠HGF = ∠AGF  ( H lies on AG)

=> ∠HGF  =  90°

Learn More:

Find angleHGF​

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