Convert 45° to radians.

We want the degrees to cancel out, so we'll use the conversion factor with degrees on the bottom.

Convert 300° to radians.

Convert radians to degrees.

This time, we wanna use the conversion factor with radians on the bottom. That'll cancel out those radians and leave us with degrees.

Find the reference angle for 225°.

Hmm...225° is in between 180° (half a circle) and 270° (three-quarters of a circle), so it falls into Quadrant III.

In Quadrant III, we use the formula ρ = ɵ – 180°.

ρ = 225° – 180° = 45°

Find the reference angle for 150°.

A 150° angle falls into Quadrant II.

In Quadrant II, we use ρ = 180° – ɵ. Let's do this thing.

ρ = 180° – 150° = 30°

Find the reference angle for 420°.

Hit the brakes: 420° doesn't fall into our 0° ≤ ɵ ≤ 360° range.

Since 420° is larger than 360°, we must subtract 360° to get our ɵ.

420° – 360° = 60°

That's in Quadrant I, so we've already got our reference angle:

ρ = ɵ = 60°