Question

I will mark the first answer brainliest so please do it fast

Answer 1

Given, EFA is a right angled triangle with angle EFA = 90° and FGB is an equilateral triangle. Find y - 2x .


solution:
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since ,angle EFA = 90°




since,we know that each angles of equilateral ∆ = 60°. so then




angle BFG = angle FBG= angle FGB = 60°





in ∆ CFG :
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x + 60° + 92° = 180°




x + 152° = 180°


x = 28°





since ,angle x = 28°





so then, angle BFC = (60 - x)°




since , angle EFA = 90°





angle EFB + angle BFC = 90°





y + (60° - x ) = 90°





y + (60 - 28°) = 90°






y +32° = 90° => y = 58°






therefore ,





y - 2x = 58° - 2 (28° )






y - 2x = 58° - 56° = 2°





Answer : y - 2x = 2°
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Answer 2

Given that ΔFGB is an equilateral triangle

∠BGF =∠GBF = ∠GFB =  60º

FInd x:

Sum of angles in a triangle is 180º

∠CFG + ∠FGC + ∠GCF = 180

x + 60 + 92= 180

x + 152 = 180

x = 28º

FInd ∠BFC:

Recall that ∠BFG is  60º

∠BFC + ∠CFG = ∠BFG

∠BFC + 28 = 60

∠BFC= 32º

Find y:

∠EFA is a 90º (Given)

∠EFB + ∠BFC = ∠EFA

y + 32 = 90

y = 58º

FInd y - 2x:

We have found that x = 28º and y = 58º

y - 2x = 58 - 2(28)

y - 2x = 58 - 56

y - 2x = 2

Answer: 2