Question

question 7 of 25 what is the value of x in the isosceles trapezoid below? a (3x + 10)° 140° d c b o a. 10 o b. 40 o c. 30 o d. 20

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, base - angles are equal. So, the angle at \(C\) and the angle at \(D\) are equal, and the angle at \(A\) and the angle at \(B\) are equal. Also, the sum of adjacent angles along a non - parallel side is \(180^{\circ}\). So, \((3x + 10)+140=180\).

Step2: Solve the equation for \(x\)

First, simplify the left - hand side of the equation: \(3x+10 + 140=3x + 150\). Then, we have the equation \(3x+150 = 180\). Subtract 150 from both sides: \(3x=180 - 150\), so \(3x = 30\). Divide both sides by 3: \(x=\frac{30}{3}=10\).

Answer:

A. 10