A single pure component is joined to a source of 15 V rms and 80 Hz…

Step 1. The period. $T = \dfrac{1}{f} = \dfrac{1}{80\ \text{Hz}} = 12.5$ ms.

Step 2. The phase. The delay is $3.1$ ms, so the fraction of a cycle is $\dfrac{3.1}{12.5} = 0.248$. The angle is $0.248 \times 360^\circ = 89^\circ$. This is $90^\circ$ within the accuracy of the reading.

Step 3. Which part? The current peak comes after the voltage peak, so the current lags by $90^\circ$. That means a coil. (A capacitor would have its current peak earlier.)

Step 4. The reactance. $X_L = \dfrac{V_{rms}}{I_{rms}} = \dfrac{15\ \text{V}}{0.060\ \text{A}} = 250\ \Omega$.

Step 5. The inductance. We want $L$, so $L = \dfrac{X_L}{2\pi f} = \dfrac{250\ \Omega}{2\pi \times 80\ \text{Hz}} = 0.497$ H.