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…

Answer:

D. $a=8; b=40$

Explanation:

Step1: Solve for $a$ using the property of equal adjacent sides.

In a kite, two pairs of adjacent sides are equal. From the figure, we assume $XY = YZ$. $$3a - 5 = a + 11$$ Subtract $a$ from both sides: $$3a - a - 5 = 11$$ $$2a - 5 = 11$$ Add 5 to both sides: $$2a = 11 + 5$$ $$2a = 16$$ Divide by 2: $$a = \frac{16}{2}$$ $$a = 8$$

Step2: Solve for $b$ using the properties of angles in a kite.

In a kite, one pair of opposite angles are equal. These are the angles between the unequal sides. In kite WXYZ, this means $\angle X = \angle Z$. Given $\angle X = (3b)^\circ$, so $\angle Z = (3b)^\circ$. The sum of the interior angles of a quadrilateral is $360^\circ$. $$\angle W + \angle X + \angle Y + \angle Z = 360^\circ$$ Substitute the given values: $$50^\circ + (3b)^\circ + 70^\circ + (3b)^\circ = 360^\circ$$ $$50 + 3b + 70 + 3b = 360$$ Combine like terms: $$120 + 6b = 360$$ Subtract 120 from both sides: $$6b = 360 - 120$$ $$6b = 240$$ Divide by 6: $$b = \frac{240}{6}$$ $$b = 40$$ Thus, $a=8$ and $b=40$.