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In the accompanying diagram, transversal EF intersects parallel lines AB and CD at G and H, respectively. If m∠EGB = 2x + 40 and m∠FHC = 3x - 10, what is the value of x

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No diagram is provided but we can still work it out (it may vary).

So the from the description, we can tell that m∠EGB = m∠FHC through alternate exterior angles.

So,

m∠EGB = 2x + 40

m∠FHC = 3x - 10

m∠EGB = m∠FHC

2x + 40 = 3x - 10

40 = 3x - 2x - 10

40 = x - 10

40 + 10 = x

50 = x

x = 50

The value of x is 50

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