Question

if trap is an isosceles trapezoid, what is the value of x? a. 9 b. 25 c. 18 d. 23 e. 19 f. cannot be determined

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, base - angles are equal. So, the sum of adjacent angles along a non - parallel side is 180°. We have the equation \(4x+(5x + 9)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+5x+9 = 9x+9\). So the equation becomes \(9x + 9=180\).

Step3: Isolate the variable term

Subtract 9 from both sides: \(9x+9 - 9=180 - 9\), which gives \(9x=171\).

Step4: Solve for x

Divide both sides by 9: \(x=\frac{171}{9}=19\).

Answer:

E. 19