Question

a =
b =
m<1 =
m<2 =

Explanation:

Step1: Determine the scale factor

Since the polygons are similar, the ratio of corresponding sides is the same. The ratio of the sides \(8\) and \(12\) is \(\frac{12}{8} = 1.5\).

Step2: Find the value of \(a\)

The side of length \(12\) in the first polygon corresponds to side \(a\) in the second polygon. Using the scale factor \(1.5\), \(a=\frac{12}{1.5}=18\)

Step3: Find the value of \(b\)

The side of length \(19.5\) in the second polygon corresponds to side \(b\) in the first polygon. Using the scale factor \(1.5\), \(b = \frac{19.5}{1.5}=13\)

Step4: Find \(m\angle1\)

Similar polygons have corresponding angles equal. So \(m\angle1 = 103^{\circ}\)

Step5: Find \(m\angle2\)

Since the first polygon has a right - angle (\(90^{\circ}\)), and similar polygons have corresponding angles equal, \(m\angle2=90^{\circ}\)

Answer:

\(a = 18\), \(b = 13\), \(m\angle1=103^{\circ}\), \(m\angle2 = 90^{\circ}\)