Question

Quadrilateral WXYZ is a square. If WT=6, find each measure?

Answer 1

We know that the diagonals of a square bisect each other which results in the formation of 4 - 90° angles . Which means ZX = 2 × WT . Then ,

= ZX = 2 × 6

= ZX = 12 ( ZX is a diagonal )

Side XY =

XY = √2 d/2

XY = √2 . 12/2

XY = 8.48528

m∠WTZ = 90° ( as the diagonals of a square intersect to form a complete angle ( 360° ) which is divided into four equal parts , each part being 90° )

m∠WTZ = 90°

m∠WYX = 45° ( WYX is half of one of the interior angles in this square which will mean it will be equal to 45° )

Therefore , m∠WYX = 45°

In short :

ZX = 12

XY = 8.48528

m∠WTZ = 90°

m∠WYX = 45°