Question

11.
solve for x.
(the image shows a hexagon with angles 100, 120, 120, 125, 125, and x at its vertices)

Explanation:

Step1: Recall the formula for the sum of interior angles of a hexagon

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

Step2: Set up an equation

Let \(x\) be the unknown angle. We know that \(100 + 120+120 + 125+125+x=720\).
Simplify the left - hand side: \((100)+(120 + 120)+(125+125)+x=100 + 240+250+x\).
\(100+240 + 250+x=590+x\).

Step3: Solve the equation for \(x\)

We have the equation \(590+x=720\).
Subtract 590 from both sides: \(x=720 - 590\).

Answer:

\(x = 130\)