Question

problem 3
polygon b is a scaled copy of polygon a.
a 2.5 1.5 2.5
b 5 53° 82°
a. what is the scale factor from polygon a to polygon b? explain your reasoning.
b. find the missing length of each side marked with ? in polygon b.
c. determine the measure of each angle marked with ? in polygon a.

Explanation:

Step1: Calculate the scale - factor

The scale factor $k$ is found by dividing the length of a side of Polygon $B$ by the corresponding side of Polygon $A$. For the given sides, if we take the side of length $5$ in Polygon $B$ and the corresponding side of length $2.5$ in Polygon $A$, then $k=\frac{5}{2.5}=2$.

Step2: Find the missing side - lengths in Polygon $B$

The vertical side of Polygon $A$ has length $1.5$. Using the scale factor $k = 2$, the length of the corresponding side in Polygon $B$ is $1.5\times2 = 3$. The other side of Polygon $A$ has length $2.5$, and the length of the corresponding side in Polygon $B$ is $2.5\times2=5$.

Step3: Determine the angle - measures in Polygon $A$

Since Polygon $B$ is a scaled - copy of Polygon $A$, corresponding angles are equal. The angle of $53^{\circ}$ in Polygon $B$ corresponds to an angle in Polygon $A$ which is also $53^{\circ}$. The angle of $82^{\circ}$ in Polygon $B$ corresponds to an angle in Polygon $A$ which is $82^{\circ}$.

Answer:

a. The scale factor from Polygon $A$ to Polygon $B$ is $2$ because $\frac{5}{2.5}=2$.
b. The missing side - lengths in Polygon $B$ are $3$ and $5$.
c. The missing angle - measures in Polygon $A$ are $53^{\circ}$ and $82^{\circ}$.