Answer :
The possible range of angle x is x < 44
How to solve for angle x
given data
In △ A B C , A B = 7 , B C = 12 , and m ∠ A B C = 82 ∘
In △ D E F , D E = 7 , E F = 12 and m ∠ D E F = ( 2 x − 6 ) ∘
A C > D F
Solution for angle x is gotten from the clue in A C > D F
This means that angle included by m ∠ A B C = 82 ∘ is greater than the angle included by m ∠ D E F = ( 2 x − 6 ) ∘
We therefore say that
82 ∘ > ( 2 x − 6 ) ∘
82 + 6 > 2 x
88 > 2 x
divide both sides by 2
88 / 2 > 2 x / 2
44 > x
x < 44 degrees
Hence option g is the correct answer
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