Question

use the diagram to solve for x. (10x - 10)° (5x + 30)° (8x - 1)° (6x - 7)° x =

Explanation:

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

The sum of the interior angles of any quadrilateral is \(360^\circ\). So we can set up the equation by adding all the given angle expressions and setting it equal to \(360\).

$$ (5x + 30)+(8x - 1)+(6x - 7)+(10x - 10)=360 $$

Step2: Combine like terms.

First, combine the \(x\) terms: \(5x+8x + 6x+10x=29x\).
Then, combine the constant terms: \(30-1 - 7-10 = 12\).
So the equation becomes:

$$ 29x+12 = 360 $$

Step3: Solve for \(x\).

Subtract \(12\) from both sides of the equation:

$$ 29x=360 - 12 $$

$$ 29x=348 $$

Divide both sides by \(29\):

$$ x=\frac{348}{29} $$

$$ x = 12 $$

Answer:

\(12\)