Question

consider kite abcd. what are the values of x and y? o x = 2, y = 22 o x = 2, y = 44 o x = 5, y = 22 o x = 5, y = 44

Explanation:

Answer:

In a kite, two - pairs of adjacent sides are equal. So \(4x - 3=2x + 7\).
\[

$$\begin{align*} 4x-2x&=7 + 3\\ 2x&=10\\ x&=5 \end{align*}$$

\]
The sum of the interior angles of a quadrilateral is \(360^{\circ}\). So \(79^{\circ}+61^{\circ}+5y^{\circ}+(360-(79 + 61+5y))^{\circ}=360^{\circ}\), and also using the angle - sum property \(79+61 + 5y+(180)=360\) (since the non - vertex angles of a kite are equal).
\[

$$\begin{align*} 79+61+5y&=180\\ 140+5y&=180\\ 5y&=40\\ y& = 44 \end{align*}$$

\]
So the answer is \(x = 5,y = 44\) which corresponds to the fourth option: \(x = 5,y = 44\)