We are given a square WXYZ and the point of intersection of the diagonals T. We want to find the measure of ∠ WYX. All four angles in a square are right angles. Let's begin by recalling that since each square is also a rhombus, each diagonal in a square bisects a pair of opposite angles.
Because the diagonal bisects ∠ XYZ, we know that m∠WYX is half of m∠XYZ. We also know that ∠ XYZ is a right angle, so its measure is 90^(∘). Let's calculate m∠ WYX by substituting 90 for m∠ XYZ.
Let's consider why the diagonals of a square bisect a pair of opposite angles. To do so, we will start by recalling and comparing the definitions of a square and a rhombus.
Type of Quadrilateral
Definition
Square
A square is a parallelogram with four congruent sides and four right angles.
Rhombus
A rhombus is a parallelogram with four congruent sides.
We can see that the definition of a square contains the definition of a rhombus. Since a square is also a rhombus, all properties of rhombuses apply to squares.
