The problem asks us to identify the type of arc $mNL$ (major arc, minor arc, or semicircle) and find its measure, given that $NL$ and $MK$ are diameters of circle $T$.

1. Problem Description

The problem asks us to identify the type of arc $mNL$ (major arc, minor arc, or semicircle) and find its measure, given that $NL$ and $MK$ are diameters of circle $T$.

2. Solution Steps

Since $NL$ is a diameter, the measure of arc $NL$ is 180 degrees. We are given that the central angle $NTM = 88^\circ$. Therefore, the arc $NM$ has a measure of 88 degrees, i.e., $mNM = 88^\circ$.

Since $NL$ is a diameter, $mNL=180^\circ$.

Also, a major arc is an arc that is greater than 180 degrees but less than 360 degrees. A minor arc is an arc that is less than 180 degrees. A semicircle is an arc that is exactly 180 degrees.

We are trying to find $mNL$. Since $NL$ is a diameter, the points $N, T,$ and $L$ are collinear, and $mNL=180^\circ$. Therefore, $mNL$ is a semicircle.

$mNL = 360 - mNM - mML = 360 - 88 - 48 = 360-136 = 224$. However, that is incorrect. We can determine $mNL$ by recognizing that $NL$ is a diameter. Thus, it makes half the circle and has an arc length of 180 degrees. Another way to see it is that $mNK = 180-88 = 92$, and then $mNL=mNK + mKL = 92 + 88=180$.

However, that interpretation of $mNL$ is incorrect because the problem defines it as arc from point $N$ to point $L$ in a CLOCKWISE fashion.

So, we calculate $mNL = 360 - mNM = 360 - 88 = 272$.

$mNL$ is the measure of the arc from $N$ to $L$ in the direction indicated by the order of the letters. Since we are going from $N$ to $L$ following $K, J, M$, the arc passes through the remaining portion of the circle besides arc $NM$. Since $mNM = 88^\circ$, $mNL = 360^\circ - 88^\circ = 272^\circ$.

Since $272^\circ > 180^\circ$, $mNL$ is a major arc.

3. Final Answer

major arc

272