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.

Find the measure of each angle indicated.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Solve for x.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Find the measure of each angle indicated.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**