Question

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

Explanation:

Step1: Use the property of equal adjacent sides in a kite

In a kite, two pairs of adjacent sides are equal. So, \(3a - 5=a + 11\).
Subtract \(a\) from both sides: \(3a-a-5=a - a+ 11\), which gives \(2a-5 = 11\).
Add \(5\) to both sides: \(2a-5 + 5=11 + 5\), so \(2a=16\).
Divide both sides by \(2\): \(a=\frac{16}{2}=8\).

Step2: Use the angle - sum property of a quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\). In kite \(WXYZ\), \(\angle W+\angle X+\angle Y+\angle Z = 360^{\circ}\). Since a kite has one pair of opposite angles equal (assuming non - vertex angles), and using the angle sum formula \(50^{\circ}+3b^{\circ}+70^{\circ}+3b^{\circ}=360^{\circ}\).
Combine like terms: \(120^{\circ}+6b^{\circ}=360^{\circ}\).
Subtract \(120^{\circ}\) from both sides: \(6b^{\circ}=360^{\circ}-120^{\circ}=240^{\circ}\).
Divide both sides by \(6\): \(b=\frac{240}{6}=40\).

Answer:

\(a = 8;b = 40\) (the fourth option)