Question

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the diagram shows a convex polygon.
what is the value of x?
x = \square^\circ

Explanation:

Step1: Recall exterior angle sum of polygon

The sum of exterior angles of any convex polygon is \(360^\circ\). So we sum all given exterior angles and set equal to \(360^\circ\).
\((2x - 50) + (2x - 49) + (3x - 3) + 2x + 57 = 360\)

Step2: Combine like terms

Combine the \(x\)-terms and constant terms:
\((2x + 2x + 3x + 2x) + (-50 - 49 - 3 + 57) = 360\)
\(9x + (-45) = 360\)

Step3: Solve for \(x\)

Add 45 to both sides:
\(9x = 360 + 45\)
\(9x = 405\)
Divide both sides by 9:
\(x = \frac{405}{9}\)
\(x = 45\)

Answer:

\(45\)