Question

use the image to answer the question. abcd is a trapezoid with $overline{ab}paralleloverline{cd}$ where $ad = 8x + 7$ and $bc = 2x + 28$. for what value of x is abcd an isosceles trapezoid? (1 point) 3.5 14.5 15 5.5

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, non - parallel sides are equal. So, we set $AD = BC$.
$$8x + 7=2x + 28$$

Step2: Isolate variable terms

Subtract $2x$ from both sides:
$$8x-2x + 7=2x-2x + 28$$
$$6x+7 = 28$$

Step3: Isolate the variable

Subtract 7 from both sides:
$$6x+7 - 7=28 - 7$$
$$6x=21$$

Step4: Solve for x

Divide both sides by 6:
$$x=\frac{21}{6}=3.5$$

Answer:

3.5