Question

1. find the value of x.

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 add up all the given exterior angles and set the sum equal to \(360\).
\((5x + 4)+(4x + 9)+(9x - 6)+(4x + 1)+(7x + 4)=360\)

Step2: Combine like terms

First, combine the \(x\) terms: \(5x+4x + 9x+4x+7x=(5 + 4+9 + 4+7)x = 29x\)
Then, combine the constant terms: \(4 + 9-6 + 1+4=(4 + 9+1 + 4)-6=18 - 6 = 12\)
So the equation becomes \(29x+12 = 360\)

Step3: Solve for \(x\)

Subtract \(12\) from both sides: \(29x=360 - 12=348\)
Divide both sides by \(29\): \(x=\frac{348}{29} = 12\)

Answer:

\(x = 12\)