Question

quadrilateral stuv is an isosceles trapezoid, su = 2y - 52, and tv = y + 24. what is the value of y? y =

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, the diagonals are equal in length. So, \( SU = TV \).

Step2: Set up the equation

Given \( SU = 2y - 52 \) and \( TV = y + 24 \), we set them equal: \( 2y - 52 = y + 24 \).

Step3: Solve for y

Subtract \( y \) from both sides: \( 2y - y - 52 = y - y + 24 \), which simplifies to \( y - 52 = 24 \).
Then add 52 to both sides: \( y - 52 + 52 = 24 + 52 \), so \( y = 76 \).

Answer:

\( 76 \)