The measure of ∠LKNM in triangle MNO is 80°.
To find the measure of ∠LKNM in triangle MNO, we first need to find the measures of the angles in triangle JKL.
We are given that ∠L = 80°, ∠J = 54°, and ∠K = 46°.
Since triangle JKL is a triangle on a plane with three angles adding up to 180°, we can find the measure of ∠L by subtracting the measures of ∠J and ∠K from 180°.
So, ∠L = 180° - (∠J + ∠K) = 180° - (54° + 46°) = 80°.
Therefore, the measure of ∠LKNM in triangle MNO is also 80°.