Question

use the diagram to solve for x.

x =

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral.

The sum of the interior angles of a quadrilateral is \(360^\circ\). So we can set up the equation by adding all the angle expressions and setting them equal to \(360\).
The angles are \((8x + 7)^\circ\), \((14x - 11)^\circ\), \((10x + 13)^\circ\), and \((5x + 18)^\circ\). So the equation is:

$$ (8x + 7)+(14x - 11)+(10x + 13)+(5x + 18)=360 $$

Step2: Combine like terms.

First, combine the \(x\) terms: \(8x+14x + 10x+5x=37x\)
Then, combine the constant terms: \(7-11 + 13+18=27\)
So the equation becomes:

$$ 37x+27 = 360 $$

Step3: Solve for \(x\).

Subtract \(27\) from both sides:

$$ 37x=360 - 27 $$

$$ 37x=333 $$

Divide both sides by \(37\):

$$ x=\frac{333}{37} $$

$$ x = 9 $$

Answer:

\(9\)