Question

13 solve for x.

Explanation:

Step1: Calculate the sum of interior angles of a hexagon

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For \(n = 6\) (a hexagon), the sum is \((6 - 2)\times180^{\circ}=720^{\circ}\).

Step2: Set up the equation

\((x + 80)+115+(x + 75)+130+(x + 50)+135=720\)
Combine like - terms: \(3x+(80 + 115+75+130+50+135)=720\)
Calculate the sum of constants: \(80+115 + 75+130+50+135 = 585\)
The equation becomes \(3x+585 = 720\)

Step3: Solve for \(x\)

Subtract \(585\) from both sides: \(3x=720 - 585\)
\(3x = 135\)
Divide both sides by \(3\): \(x=\frac{135}{3}=45\)

Answer:

\(45\)