Question

determine m∠cpx. make sure to reset the tool before determining this measure. rotate ab to create ∠xpb that measures 120°. rotate 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 th 180°. | m∠bpc | m∠dpa | m∠cpa | m∠bpd | | 100° | 100° | | |

Explanation:

Step1: Analyze the angle ∠CPX

We know that ∠XPC is given as 20°, and ∠CPX is the same as ∠XPC but in the opposite direction? Wait, no. Wait, the angle ∠CPX: let's think about the notation. ∠CPX means the angle at point P between points C, P, X. Wait, but we have ∠XPC which is 20°. Wait, maybe there's a typo or maybe we need to consider the straight line or the angle relationship. Wait, no, the problem says "Rotate CD to create ∠XPC that measures 20°". So ∠XPC is 20°, but ∠CPX is the same angle as ∠XPC? Wait, no, angle notation: ∠XPC is at P, with segments XP and PC. ∠CPX is also at P, with segments CP and PX. So they are the same angle. Wait, but maybe I misread. Wait, the first rotation: "Rotate AB to create ∠XPB that measures 120°". So ∠XPB is 120°, which is at P, with segments XP and PB. Then ∠XPC is 20°, at P, with segments XP and PC. So if we consider the angles around point P, but maybe we need to find ∠CPX. Wait, ∠XPC is 20°, so ∠CPX is also 20°? Wait, no, maybe the problem is that ∠XPB is 120°, and ∠XPC is 20°, so ∠CPB would be ∠XPB - ∠XPC = 120° - 20° = 100°, which matches the table's m∠BPC = 100°. But the question is m∠CPX. Wait, ∠XPC is 20°, so ∠CPX is equal to ∠XPC? Wait, no, angle ∠CPX: the order of the letters is C, P, X, so the angle is at P between C and X. ∠XPC is at P between X and C. So they are the same angle, just named in reverse. So the measure should be 20°? Wait, but maybe I made a mistake. Wait, let's check again. The problem says "Rotate CD to create ∠XPC that measures 20°". So ∠XPC = 20°, so ∠CPX is the same as ∠XPC, so m∠CPX = 20°? Wait, but maybe the problem is different. Wait, maybe the angle is supplementary? No, the problem says the correct measure is less than 180°. Wait, maybe I misread the angle. Wait, the first rotation: ∠XPB is 120°, which is XP to PB. The second rotation: ∠XPC is 20°, XP to PC. So if PC is between XP and PB, then ∠CPB is 120° - 20° = 100°, which is m∠BPC = 100°, as in the table. Then ∠CPX: let's see, ∠XPC is 20°, so ∠CPX is 20°? Wait, maybe the answer is 20°. Wait, but let's confirm. The problem says "Determine m∠CPX". The rotation for CD creates ∠XPC = 20°, so ∠CPX is the same as ∠XPC, so measure is 20°.

Step2: Confirm the angle

Since ∠XPC is given as 20°, and ∠CPX is the same angle (just named with the vertex in the middle and the other two points reversed), the measure of ∠CPX is equal to the measure of ∠XPC, which is 20°.

Answer:

20°