Question

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.

m∠abc=

m∠bcd=

m∠dea=

m∠cde=

Explanation:

Step1: Use the property of rotation

Rotation is a rigid transformation. Rigid transformations (like rotation) preserve the measures of angles. So, the angles of polygon \(ABCDE\) are congruent to the corresponding angles of polygon \(FGHIJ\).

Step2: Identify corresponding angles

• \(\angle ABC\) corresponds to \(\angle GHI\). Since \(m\angle GHI = 90^{\circ}\), then \(m\angle ABC=90^{\circ}\).
• \(\angle BCD\) corresponds to \(\angle G\). Since \(m\angle G = 117^{\circ}\), then \(m\angle BCD = 117^{\circ}\).
• \(\angle DEA\) corresponds to \(\angle I\). Since \(m\angle I=127^{\circ}\), then \(m\angle DEA = 127^{\circ}\).
• \(\angle CDE\) corresponds to \(\angle F\). Since \(m\angle F = 117^{\circ}\), then \(m\angle CDE=117^{\circ}\).

Answer:

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