Question

question 2 (1 point)
polygon b is a scaled copy of polygon a.
what is the scale factor from polygon a to polygon b? explain your reasoning.
find the missing length of each side marked with ? in polygon b.
determine the measure of each angle marked with ? in polygon a.
images: polygon a (top) with sides 2.5, 1.5, 2.5, two angles ?; polygon b (bottom) with side 5, angle 53°, angle 82°, sides ? and ?

Explanation:

Part 1: Scale Factor from Polygon A to Polygon B

Step 1: Identify Corresponding Sides

We take the length of a side in Polygon B and divide it by the corresponding side in Polygon A. For the top side, Polygon A has length \( 2.5 \) and Polygon B has length \( 5 \).

Step 2: Calculate Scale Factor

The scale factor \( k \) is given by \( k=\frac{\text{Length in B}}{\text{Length in A}} \). So, \( k = \frac{5}{2.5}=2 \).

Step 1: Use Scale Factor

The scale factor is \( 2 \), so we multiply the length in A (\( 1.5 \)) by the scale factor.

Step 2: Calculate Length

Length in B \( = 1.5\times2 = 3 \).

Step 1: Use Scale Factor

Multiply the length in A (\( 2.5 \)) by the scale factor (\( 2 \)).

Step 2: Calculate Length

Length in B \( = 2.5\times2 = 5 \).

Answer:

The scale factor is \( 2 \).

Part 2: Missing Lengths in Polygon B

Vertical Side (Corresponding to 1.5 in A)