Question

mathematical connections the two polygons are similar. find the values of x and y. x = y =

Explanation:

Step1: Find the value of \(x\)

Since the two polygons are similar, the ratios of corresponding sides are equal.
We have the proportion \(\frac{x}{5}=\frac{6}{4}\).
Cross - multiply: \(4x = 6\times5\).
\(4x=30\), then \(x=\frac{30}{4}=\frac{15}{2}=7.5\).

Step2: Find the value of \(y\)

The sum of the interior angles of a quadrilateral is \(360^{\circ}\).
For the second quadrilateral (lower one), we know three angles: \(90^{\circ},116^{\circ},61^{\circ}\).
The fourth angle is \(360-(90 + 116+61)=360 - 267 = 93^{\circ}\).
For the first quadrilateral (upper one), we have the equation \(y-73=93\).
Add 73 to both sides: \(y=93 + 73=166\).

Answer:

\(x = 7.5\), \(y = 166\)