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 property of a kite's 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 $\angle Y$. So, $50^{\circ}+70^{\circ}+3b + 3b=360^{\circ}$.

Step2: Solve the angle - sum equation for $b$

First, simplify the left - hand side of the equation: $120^{\circ}+6b = 360^{\circ}$. Then subtract $120^{\circ}$ from both sides: $6b=360^{\circ}- 120^{\circ}=240^{\circ}$. Divide both sides by 6: $b = 40$.

Step3: Use property of a kite's sides

In a kite, two pairs of adjacent sides are equal. Let's assume $XY = YZ$. So, $3a−5=a + 11$.

Step4: Solve the side - length equation for $a$

Subtract $a$ from both sides: $3a−a−5=a−a + 11$, which gives $2a−5 = 11$. Add 5 to both sides: $2a=11 + 5=16$. Divide both sides by 2: $a = 8$.

Answer:

$a = 8, b = 40$