The problem asks us to identify whether arc $JL$ is a major arc, a minor arc, or a semicircle, and to find its measure. We are given that $NL$ and $MK$ are diameters of circle $T$. We are also given that $\angle NTJ = 88^\circ$, $\angle JTK = 44^\circ$, and $\angle KTL = 48^\circ$.

GeometryGeometryCirclesArcsAnglesCentral Angle
2025/5/4

1. Problem Description

The problem asks us to identify whether arc JLJL is a major arc, a minor arc, or a semicircle, and to find its measure. We are given that NLNL and MKMK are diameters of circle TT. We are also given that NTJ=88\angle NTJ = 88^\circ, JTK=44\angle JTK = 44^\circ, and KTL=48\angle KTL = 48^\circ.

2. Solution Steps

First, we need to find the measure of arc JLJL. The measure of arc JLJL is equal to the measure of the central angle JTL\angle JTL.
We can find the measure of JTL\angle JTL by adding the measures of JTK\angle JTK and KTL\angle KTL.
JTL=JTK+KTL\angle JTL = \angle JTK + \angle KTL
JTL=44+48\angle JTL = 44^\circ + 48^\circ
JTL=92\angle JTL = 92^\circ
Since the measure of arc JLJL is 9292^\circ, and 0<92<1800^\circ < 92^\circ < 180^\circ, arc JLJL is a minor arc.

3. Final Answer

Arc JLJL is a minor arc.
The measure of arc JLJL is 9292^\circ.

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