Question

find the value of x. x =

Explanation:

Step1: Use the formula for the sum of interior angles of a polygon

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

Step2: Set up an equation

We have \(4x+90 + 90=720\) (since there are two right - angles (\(90^{\circ}\) each) and four angles of measure \(x\)).
Simplify the equation: \(4x+180 = 720\).
Subtract \(180\) from both sides: \(4x=720 - 180\).
So, \(4x = 540\).
Divide both sides by \(4\): \(x=\frac{540}{4}=135\).

Answer:

\(135\)