Question

1. find ( mangle vwz )

Explanation:

Step1: Use rectangle angle property

In a rectangle, $\angle VYX = 90^\circ$, so $\angle VXY + \angle XVY = 90^\circ$. Substitute the given angles:
$(5x-12)^\circ + (2x-3)^\circ = 90^\circ$

Step2: Solve for x

Combine like terms and isolate x:
$7x - 15 = 90$
$7x = 105$
$x = 15$

Step3: Identify triangle VWZ properties

In rectangle VWXY, diagonals bisect each other, so $VW = XZ$ and $VZ = WZ$, making $\triangle VWZ$ isosceles. $\angle VWZ = \angle WVZ$. Also, $\angle WVZ = \angle VXY = (2x-3)^\circ$ (alternate interior angles).

Step4: Calculate $\angle VWZ$

Substitute $x=15$ into $(2x-3)^\circ$:
$2(15) - 3 = 30 - 3 = 27$

Answer:

$27^\circ$