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In triangle DEF, if [tex]m\angle D = (2x)^\circ[/tex], [tex]m\angle E = (2x - 4)^\circ[/tex], and [tex]m\angle F = (x + 9)^\circ[/tex], what is the value of x?

A. 35
B. 37
C. 44
D. 71

Answer :

Final answer:

The value of x in triangle DEF is 35.

Explanation:

To find the value of x in triangle DEF, we need to set up an equation using the given angle measures. Since the sum of angles in a triangle is 180 degrees, we can set up the equation (2x) + (2x - 4) + (x + 9) = 180. Simplifying this equation gives us 5x + 5 = 180. Solving for x, we subtract 5 from both sides giving us 5x = 175. Finally, dividing both sides by 5, we find that x = 35. Therefore, the value of x is 35.

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