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A car enters a curve in the road with a speed of 32 m/s and emerges from this curve 4 s later with the same speed. However, the direction of the velocity changes by 150 degrees during this time. What is the magnitude of the average acceleration during this time interval?

My question is, that how are we supposed to calculate the radius when we only have angle. We don't even know the length of curve

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We don’t need to know the length of the curve or its radius. We have

$$\displaystyle \text{average acceleration} = \frac{|\Delta \vec v|}{t}$$

We know the change in velocity $\Delta \vec v$ and the time period $t$ so we have everything we need to find the average acceleration.

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