On a still day, rain falls straight down at 9 m/s…

Step 1. Relative velocity. $\vec{v}_{\text{rain}} - \vec{v}_{\text{Nikhil}}$: $9\ \text{m/s}$ down, and $4\ \text{m/s}$ backwards, towards his face.

Step 2. Angle. $\tan\theta = \dfrac{4\ \text{m/s}}{9\ \text{m/s}}$, so $\theta = 24.0^\circ$ from the vertical. He tilts the umbrella forward by $24^\circ$.

Step 3. Speed. $\sqrt{(9\ \text{m/s})^2 + (4\ \text{m/s})^2} = 9.85\ \text{m/s}$.

Step 4. With the wind. The rain now moves forward at $4\ \text{m/s}$, just as he does. Relative to him it has no forward or backward part, so it seems to fall straight down at $9\ \text{m/s}$. He holds the umbrella upright.