Question

In a trapezium ABCD, bisectors of angles A, B, C and D form a quadrilateral
EFGH as shown. Find angleHGF​

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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Answer 2

Step-by-step explanation:

Question ::-

In a trapezium ABCD, bisectors of angles A, B, C and D form a quadrilateral

EFGH as shown

To Find ::-

Find angle HGF?

Solution ::-

Trapezium ABCD

AB ll 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 ΔADG

➡ ∠DAG + ∠ADG + ∠AGD = 180°

➡ ∠A/2 + ∠D/2 + ∠AGD = 180°

➡ (∠A + ∠D)/2 + ∠AGD = 180°

➡ 90° + ∠AGD = 180°

➡ ∠AGF + ∠AGD = 180° [Linear Pair]

➡ ∠AGF = 90°

∠HGF = ∠AGF [H lies on AG]

➡∠HGF = 90°

⭐️Read More :

The trapezium is a quadrilateral with two parallel sides. The parallel sides of a trapezium are called bases and the non-parallel sides of a trapezium are called legs. It is also called a trapezoid. Also, 'h' is the distance between the two parallel sides which demonstrates the height of the trapezium.

Hope it helpful . ✌️

@Somya2563