Question

quadrilateral hijk is an isosceles trapezoid, hj = 2a + 24, and ik = 8a - 24. what is the value of a?

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, the non - parallel sides are equal. Here, assume $HJ$ and $IK$ are the non - parallel sides, so $HJ = IK$.
$2a + 24=8a - 24$

Step2: Isolate variable terms

Subtract $2a$ from both sides of the equation:
$2a+24 - 2a=8a - 24-2a$
$24 = 6a-24$

Step3: Isolate the term with $a$

Add 24 to both sides of the equation:
$24 + 24=6a-24 + 24$
$48 = 6a$

Step4: Solve for $a$

Divide both sides by 6:
$\frac{48}{6}=\frac{6a}{6}$
$a = 8$

Answer:

$8$