Question

consider kite wxyz. what are the values of a and b? o a = 4; b = 10 o a = 4; b = 40 o a = 8; b = 10 o a = 8; b = 40

Explanation:

Step1: Use property of kite sides

In a kite, two pairs of adjacent - sides are equal. So, \(3a - 5=a + 11\).
\[3a-5=a + 11\]
\[3a-a=11 + 5\]
\[2a=16\]
\[a = 8\]

Step2: Use property of kite angles

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). In a kite, one pair of non - vertex angles are equal. Let's assume the non - vertex angles are \(\angle W\) and \(\angle Y\).
The sum of the angles: \(50^{\circ}+70^{\circ}+3b^{\circ}+3b^{\circ}=360^{\circ}\)
\[120^{\circ}+6b^{\circ}=360^{\circ}\]
\[6b^{\circ}=360^{\circ}-120^{\circ}\]
\[6b^{\circ}=240^{\circ}\]
\[b = 40\]

Answer:

\(a = 8;b = 40\)