Question

question 24 of 25 what is the value of x in the isosceles trapezoid below? d c 9x° a (4x + 37)° b a. 15 b. 11 c. 81 d. 41

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. So, \(9x=4x + 37\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(9x-4x=4x + 37-4x\), which gives \(5x=37\). Then divide both sides by 5: \(x=\frac{37}{5}=7.4\) (This is wrong. Let's assume the non - parallel sides are equal and use the property of supplementary angles). In an isosceles trapezoid, adjacent angles along a non - parallel side are supplementary. So, \(9x+(4x + 37)=180\).

Step3: Combine like terms

\(9x+4x+37 = 180\), which simplifies to \(13x+37=180\).

Step4: Isolate the variable term

Subtract 37 from both sides: \(13x+37 - 37=180 - 37\), getting \(13x=143\).

Step5: Solve for \(x\)

Divide both sides by 13: \(x = 11\).

Answer:

B. 11