Question

select the correct answer from each drop - down menu.polygon abcde rotates 45° clockwise about point f to form polygon fghij, shown in the figure. find the measure of each angle of polygon abcde.( mangle abc=)( mangle bcd=)( mangle dea=)( mangle cde=)

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation. Rigid transformations (such as rotation) preserve the shape and size of the figure. So, the corresponding angles of the pre - image (polygon \(ABCDE\)) and the image (polygon \(FGHIJ\)) are equal.

Step2: Identify the corresponding angles

• \(\angle ABC\) corresponds to \(\angle GHI\). So, \(m\angle ABC = 90^{\circ}\)
• \(\angle BCD\) corresponds to \(\angle HIJ\). So, \(m\angle BCD=127^{\circ}\)
• \(\angle DEA\) corresponds to \(\angle JFG\). So, \(m\angle DEA = 90^{\circ}\)
• \(\angle CDE\) corresponds to \(\angle FGH\). So, \(m\angle CDE = 117^{\circ}\)

Answer:

\(m\angle ABC = 90^{\circ}\), \(m\angle BCD = 127^{\circ}\), \(m\angle DEA=90^{\circ}\), \(m\angle CDE = 117^{\circ}\)