Question

EFG is a triangle
HJ is parallel to FG
Angle FEG =75
Angle EFG =2x and angle FGE =(x-15)

find value of x
and
find angle HJG
​

Answer 1

Step-by-step explanation:

Let us extend the line GH to N such that it intersects the line AB at M

AB∣∣CD and GM is transversal

⟹ The ∠AMH=∠CHG=60

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(Corresponding Angles )

∠NMB=∠AMH=60

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(Vertically opposite angles)

AB∣∣CD and HK is transversal

⟹ The ∠AKH=∠KHD=25

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(Alternate interior Angles )

NM∣∣KL and KM is transversal

⟹ The ∠NMK=∠LKB=60

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(Corresponding Angles )

⟹∠LKM=180

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−∠KLB (Linear pair)

⟹∠LKM=180−60=120

∘

⟹∠HKL=∠HKA+∠AKL

⟹∠HKL=25+120=145

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