Question

quadrilateral jklm is rotated 90° clockwise about the origin to produce quadrilateral jklm.
which statement is true?
a the measure of angle m is 60°
b the measure of angle m is 80°.
c the measure of angle m is 100°.
d the measure of angle m is 120°.

Explanation:

Step1: Recall rotation property

A rotation is a rigid transformation, which means it preserves the shape and size of the figure, including the measures of angles. So, the angle measures of the original quadrilateral \(JKLM\) will be the same as those of the rotated quadrilateral \(J'K'L'M'\).

Step2: Identify angle at \(M\)

In quadrilateral \(JKLM\), the measure of angle \(M\) is \(60^\circ\) (as given in the diagram: \(\angle JML = 60^\circ\)? Wait, no, looking at the diagram, the angle at \(M\) (vertex \(M\)) is \(60^\circ\). When we rotate the quadrilateral \(90^\circ\) clockwise about the origin to get \(J'K'L'M'\), the angle at \(M'\) (corresponding to angle \(M\) in \(JKLM\)) will have the same measure as angle \(M\) in \(JKLM\).

Wait, let's correct: The original quadrilateral \(JKLM\) has angle at \(M\) as \(60^\circ\) (from the diagram: the angle between \(MMJ\) and the x - axis is \(60^\circ\), so angle at \(M\) is \(60^\circ\)). Since rotation is a rigid transformation, \(\angle M'=\angle M = 60^\circ\).

So, among the options, option A says the measure of angle \(M'\) is \(60^\circ\), which is correct.

Answer:

A. The measure of angle \(M'\) is \(60^\circ\)