Question

the figure below is a kite. solve for w, x, and y

Explanation:

Step1: Use the property of kite

In a kite, one diagonal is bisected by the other. Here, \( w = 1.6\) (given directly from the figure as one part of the bisected diagonal).

Step2: Use the property of vertical angles

Vertical angles are equal. So \( x = 48\) (as the angle opposite is \( 48^{\circ}\), vertical angles are congruent).

Step3: Use the SSS (Side - Side - Side) congruence of triangles in kite

Triangles formed by the diagonals of a kite are congruent. For the two right - angled triangles (formed by the diagonals), we can use the Pythagorean theorem. Let's consider the two triangles with sides \(3.0\), part of the diagonal and \(y\). Also, for the other pair of triangles with sides \(3.4\), \(1.6\) (half of the bisected diagonal) and the other half of the other diagonal. But since the triangles are congruent (by SSS, as two sides of the triangles formed by the diagonals of a kite are equal: two pairs of adjacent sides of the kite are equal and the diagonal is common). So \(y = 3.4\) (because in a kite, two pairs of adjacent sides are equal, \(LY = LE\) and \(FY=FE\), and from the given side lengths \(LY = 3.0\), \(LF = 3.4\), so \(FE=LF = 3.4\)).

Answer:

\(w = 1.6\), \(x = 48\), \(y = 3.4\)