Question

find the value of x .
x = 8 ×

Explanation:

Step1: Recall the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^\circ\). So we can set up an equation by adding all the given exterior angles and solving for \(x\).
The exterior angles are \(45^\circ\), \(40^\circ\), \(x^\circ\), \(77^\circ\), and \(2x^\circ\). So the equation is:
\(45 + 40 + x + 77 + 2x = 360\)

Step2: Combine like terms

Combine the constant terms and the terms with \(x\):
\((45 + 40 + 77)+(x + 2x)=360\)
\(162 + 3x = 360\)

Step3: Solve for \(x\)

Subtract \(162\) from both sides:
\(3x = 360 - 162\)
\(3x = 198\)
Divide both sides by \(3\):
\(x=\frac{198}{3}\)
\(x = 66\)

Answer:

\(x = 66\)