Quadrilaterals are polygons with exactly four sides and four angles.  One of the facts about a quadrilateral that we need to understand is that the sum of the four angles in a quadrilateral is always \(360^\circ \). That is, if you add up each of the four angles in a quadrilateral, the total measure is \(360^\circ \).

EXAMPLE:  Solve for \(x\).


SOLUTION:  The figure in this problem is a quadrilateral.  Then all four of the angles in this quadrilateral will add up to \(360^\circ \). That is,

\(70^\circ  + \left( {23x - 5} \right)^\circ  + 110^\circ  + \left( {14x} \right)^\circ  = 360^\circ \)

Simplifying the left side of this equation, we obtain

\(70^\circ  + \left( {23x - 5} \right)^\circ  + 110^\circ  + \left( {14x} \right)^\circ  = 360^\circ \)
\(37x + 175^\circ = 360^\circ \)
\(37x = 185^\circ \)
\(x = 5^\circ \)

So \(x = 5^\circ \).



EXAMPLE:  Solve for \(x\).



SOLUTION:  Again, the object in question is a quadrilateral.  If we add up all four angles in this quadrilateral, the sum will be \(360^\circ \). That is,

\(\left( {24x + 3} \right)^\circ  + 86^\circ  + 75^\circ  + 100^\circ  = 360^\circ \)
\(24x + 264^\circ  = 360^\circ \),
\(24x = 96^\circ \)
\(x = 4^\circ \)

Below you can download some free math worksheets and practice.