Question

12
type the correct answer in the box.
find the value of x in this polygon.
127°
166°
112°
93°
76°
123°
113°

Explanation:

Step 1: 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), \((6 - 2)\times180^{\circ}=720^{\circ}\).

Step 2: Set up the equation

\(93^{\circ}+160^{\circ}+127^{\circ}+112^{\circ}+123^{\circ}+113^{\circ}+x^{\circ}+76^{\circ}=720^{\circ}\).
First, sum the known angles: \(93 + 160+127+112+123+113+76=(93 + 160)+(127+112)+(123+113)+76=253+239+236+76=(253+239)+(236+76)=492+312 = 804\).
Then the equation becomes \(804 + x=720\).

Step 3: Solve for \(x\)

\(x=720 - 804+180\) (because we double - counted the angles at the split; actually, the sum of angles in the two - part polygon is still the sum of the hexagon's interior angles).
\(x = 66\).

Answer:

\(66\)