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Step 1: As we know the sum of the interior angles of a quadrilateral is equal to 360⁰. So, when we add up the given angles, they must be equal to 360⁰.

Step 2: So we get an equation as:

\[\]$\begin{align}

& 4x{}^\circ +5(x+2){}^\circ +(7x-20){}^\circ +6(x+3){}^\circ =360{}^\circ \\

& \Rightarrow 4x+5x+10+7x-20+6x+18=360 \\

& \Rightarrow 22x+8=360 \\

& \Rightarrow 22x=352 \\

& \Rightarrow x=16 \\

& \therefore x=16{}^\circ \\

\end{align}$

Step 3: Now, placing the value of x in the given angles, we get the value of each angle.

$\begin{align}

& 4x{}^\circ =4\times 16{}^\circ =64{}^\circ \\

& 5(x+2){}^\circ =5(16+2){}^\circ =90{}^\circ \\

& (7x-20){}^\circ =(7\times 16-20){}^\circ =92{}^\circ \\

& 6(x+3){}^\circ =6(16+3){}^\circ =114{}^\circ \\

\end{align}$

Thus, the four angles of the quadrilateral are 64⁰, 90⁰, 92⁰ and 114⁰.

Thus, the angles are properly calculated. These kinds of questions are easy to solve and are seen frequently in different exams. Students should know that the sum of the angles of a quadrilateral is 360⁰. You can also look up the sum of angles of other geometrical shapes too; such as for a triangle, it is 180⁰, for pentagon, it is 540⁰, for hexagon it is 720⁰. This knowledge will always come in handy for all the students.