Question

solve for x and y.
128°
x =
y =

Explanation:

Step1: Use the property of a kite (assuming it's a kite - two pairs of adjacent sides equal)

The sum of interior angles of a quadrilateral is \(360^{\circ}\). In a kite, one pair of opposite angles are equal. Let's assume the given figure is a kite. Let the angle opposite to \(128^{\circ}\) be \(128^{\circ}\) (if it's a kite). Then \(x + y+128^{\circ}+128^{\circ}=360^{\circ}\). Also, in a kite, \(x = y\) (if the non - equal angles are \(128^{\circ}\) and the other two angles \(x\) and \(y\) are equal).

Step2: Solve the equation

Substitute \(x = y\) into \(x + y+128^{\circ}+128^{\circ}=360^{\circ}\). We get \(2x+256^{\circ}=360^{\circ}\). Then \(2x=360^{\circ}-256^{\circ}=104^{\circ}\). So \(x=\frac{104^{\circ}}{2}=52^{\circ}\). Since \(x = y\), \(y = 52^{\circ}\).

Answer:

\(x = 52^{\circ}\)
\(y = 52^{\circ}\)