Use properties of rectangles to find unknown angle measures and side lengths

In the figure below, quadrilateral WXYZ is a rectangle. Find \(m(\angle YXW)\).

In rectangle WXYZ (below), \(WZ = 8\) in. Find \(m(XY)\).

In rectangle WXYZ, point \(A\) is where the diagonals intersect. Given \(WA = 5\) in, find \(m(WY)\).

In rectangle WXYZ, diagonal \(WY = 10\) in. Find \(m(XZ)\).

In the figure, quadrilateral RSTU is a rectangle with \(RS = 12\) ft and diagonal \(RT = 13\) ft. Find \(m(\angle SRU)\).

In rectangle RSTU, \(RS = 12\) ft and diagonal \(RT = 13\) ft. Find \(m(ST)\).

Hint: Triangle \(RST\) is a right triangle with the right angle at \(S\).

In rectangle RSTU, diagonal \(RT = 13\) ft and \(G\) is the point where the diagonals intersect. Find \(m(TG)\).

In the same rectangle RSTU, diagonal \(RT = 13\) ft and \(G\) is the intersection of the diagonals. Find \(m(SG)\).

A carpenter is building a shed with a 9-ft by 12-ft rectangular foundation. The four sides are already in place but the carpenter needs to verify that all four corners are right angles.

Which single measurement guarantees the foundation has four right-angle corners?