To determine who cut the larger piece of pie, we need to compare the size of the two pieces.
Since Miguel's piece is not described in terms of angle, we cannot compare the size of his piece to Mariah's piece directly in terms of their angles. Instead, we can use the fact that the area of a circular sector (a "pie slice") is proportional to the angle that the sector subtends at the center of the circle, and to the square of the radius of the circle:
Area of sector = (θ/360) x πr^2
where θ is the angle of the sector in degrees, and r is the radius of the circle.
Let's assume that the two pieces of pie have the same radius r.
If we assume that the original pie was a complete circle, then it had an angle of 360 degrees, and we can calculate the area of the whole pie as follows:
Area of whole pie = (360/360) x πr^2 = πr^2
Since Miguel's piece is not described in terms of angle, let's assume that it has a central angle of 300 degrees (i.e., he cut a sector with an angle of 300 degrees). The area of Miguel's piece is then:
Area of Miguel's piece = (300/360) x πr^2 = 5/6 x πr^2
Now consider Mariah's piece. We are told that she cut a sector with an angle of 60 degrees. The area of her piece is:
Area of Mariah's piece = (60/360) x πr^2 = 1/6 x πr^2
Since 5/6 is greater than 1/6, Miguel's piece is larger than Mariah's piece.
Therefore, we can conclude that Miguel cut the larger piece of pie.