Question

solve for x

question 6 1 pts
solve for x:

Explanation:

First Problem (Trapezoid BCDE)

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

The sum of the interior angles of any quadrilateral is \(360^\circ\). So we add up all the given angles and set the sum equal to \(360^\circ\).
The angles are \(106^\circ\), \(95^\circ\), \(74^\circ\), and \(10x - 5\). So the equation is:
\(106 + 95 + 74 + (10x - 5) = 360\)

Step2: Simplify the left - hand side of the equation.

First, add the constant terms: \(106+95 = 201\), \(201 + 74=275\), \(275-5 = 270\). So the equation becomes:
\(270+10x=360\)

Step3: Solve for x.

Subtract 270 from both sides of the equation:
\(10x=360 - 270\)
\(10x = 90\)
Divide both sides by 10:
\(x=\frac{90}{10}=9\)

Second Problem (Quadrilateral WXYZ)

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

The sum of the interior angles of a quadrilateral is \(360^\circ\). The angles are \(109^\circ\), \(71^\circ\), \(109^\circ\), and \(24x - 1\). So the equation is:
\(109+71 + 109+(24x - 1)=360\)

Step2: Simplify the left - hand side of the equation.

First, add the constant terms: \(109 + 71=180\), \(180+109 = 289\), \(289-1 = 288\). So the equation becomes:
\(288+24x=360\)

Step3: Solve for x.

Subtract 288 from both sides:
\(24x=360 - 288\)
\(24x = 72\)
Divide both sides by 24:
\(x=\frac{72}{24}=3\)

Answer:

For the first trapezoid (BCDE): \(x = 9\)
For the second quadrilateral (WXYZ): \(x = 3\)