Question

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

Explanation:

Step1: Property of kite's diagonal

In a kite, one diagonal bisects the other diagonal. So \(w = 1.6\) cm (since the diagonal \(FY\) is bisected by \(LR\)).

Step2: Property of kite's angles

In a kite, one diagonal bisects the vertex angles. So \(x = 48^{\circ}\) (since diagonal \(FY\) bisects \(\angle LFE\) and \(\angle LYE\)).

Step3: Use Pythagorean theorem

For the right - triangle formed (e.g., \(\triangle LRF\) and \(\triangle LRY\)), we know that in a kite, the diagonals are perpendicular. Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). In \(\triangle LRF\), \(c = 3.4\) cm, \(a = 1.6\) cm, then \(b=\sqrt{3.4^{2}-1.6^{2}}=\sqrt{(3.4 + 1.6)(3.4 - 1.6)}=\sqrt{5\times1.8}=\sqrt{9}=3\) cm.
For the other right - triangle (e.g., \(\triangle ERY\)), since the diagonals of a kite are perpendicular, and using the Pythagorean theorem again. Let's assume the other part of the vertical diagonal. The length of the part of the vertical diagonal adjacent to \(F\) is \(3\) cm (from above calculation). Since the diagonals of a kite: if we consider the symmetry, \(y = 3.0\) cm.

Answer:

\(w = 1.6\) cm, \(x = 48^{\circ}\), \(y = 3.0\) cm