Question

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find the value of the variable. x = (simplify your answer.) the diagram shows two lines intersecting at a point, forming angles (2x^circ) and ((84 - x)^circ).

Explanation:

Answer:

To solve for \( x \), we recognize that \( \angle AED = 2x^\circ \) and \( \angle BEC = (84 - x)^\circ \) are vertical angles. Vertical angles are equal, so we set up the equation:

\[
2x = 84 - x
\]

Add \( x \) to both sides:

\[
3x = 84
\]

Divide both sides by 3:

\[
x = 28
\]

So the value of \( x \) is \( \boxed{28} \).