Question

determine m∠cpx. make sure to reset the tool before determining this measure.
rotate \overleftrightarrow{ab} to create ∠xpb that measures 120°.
rotate \overleftrightarrow{cd} to create ∠xpc that measures 20°.
you can also press the 1 button in the explore tool to rotate the lines to the correct positions.
count to determine the measure of each angle. the correct measure of each angle will be less than 180°.

m∠bpc	m∠dpa	m∠cpa	m∠bpd

Explanation:

Step1: Analyze the given angle for ∠CPX

We are told to rotate \( \overleftrightarrow{CD} \) to create \( \angle XPC \) that measures \( 20^\circ \). Notice that \( \angle CPX \) and \( \angle XPC \) are the same angle (just named with vertices in reverse order, so their measures are equal).

Step2: Determine the measure of \( \angle CPX \)

Since \( m\angle XPC = 20^\circ \), and \( \angle CPX \) is the same as \( \angle XPC \) (angle measure is independent of the order of naming the vertices as long as the middle letter is the vertex), we have \( m\angle CPX=m\angle XPC = 20^\circ \).

Answer:

\( 20 \)