Final answer:
The values of x and y that make lines AB and CD perpendicular at their intersection point are x = 19 and y = 30.5, as this sets their intersecting angles to be 90 degrees.
Step-by-step explanation:
From the provided problem, we are given that AB is perpendicular to CD, and they intersect at point E, creating angles AED and CEB. Given that AB and CD are perpendicular, this means that the angles formed by their intersection are right angles - specifically ∠AED and ∠CEB.
This means that the measures of these angles should be 90°. We are given that ∠AED=(6x−24)° and ∠CEB=(4y-32)°. Setting these equal to 90 gives us two equations to solve for x and y. For x, the equation is 6x - 24 = 90. Solving this gives us: x = (90+24)/6 = 19. The equation for y is 4y - 32 = 90. Solving this gives: y = (90+32)/4 = 30.5
So the values of x and y that make AB perpendicular to CD are x = 19 and y = 30.5.
Learn more about Intersecting Perpendicular Lines