If ΔMNP is equilateral, how did Casey draw the arcs that defined points M and N?

The given angles are

M = 64

N = 48

where P is unknown. While we don't know P at first, we can solve for it. Recall that for any triangle, the three angles always add to 180 degrees

M+N+P = 180

64+48+P = 180

112+P = 180

112+P-112 = 180-112

P = 68

So in summary so far

M = 64

N = 48

P = 68

The shortest side is opposite the smallest angle. The side MP is opposite the smallest angle N = 48

The longest side is going to be opposite the largest angle. In this case, side MN is opposite the largest angle P = 68

The medium side is opposite the medium angle. So NP is the medium side length

Final Answers:

Shortest Side = MP

Medium Side = NP

Longest Side = MN

See the attached image for a visual summary

The ascending order would be: MP, NP, MN

Note: Something like MP is the same as PM. The order of endpoints for any given individual segment doesn't matter

Step-by-step explanation: #need any questions answered within mins/ secs hit me up and I got you

#brainliest

:)  <3