Question

what is the value of x? *
156 degrees
108 degrees
100 degrees
90 degrees

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 the equation

Let the unknown angle be \(x\). Then \(x+166 + 108+121+135 + 90=720\).

Step3: Simplify the left - hand side of the equation

First, add the known angles: \(166+108+121+135 + 90=(166+108)+(121+135)+90=274+256+90=620\).
The equation becomes \(x + 620=720\).

Step4: Solve for \(x\)

Subtract 620 from both sides of the equation: \(x=720 - 620\).

Answer:

\(100\) degrees