The tool Modify -> Divide is what you need for this.
With snap on endpoints activated, the divide tool snaps at 0°, 90°, 180° and 270°.
And with snap middle activated, you can snap in the middle of each 90° segment.
Snap middle has also an option in tool option bar, where you can set the number of middle points.
With 1 middle point snap is at 45°, with 2 points it snaps on 30° and 60° etc.
Or draw an angle line with the needed angle and use snap on intersection.
investing less than half an hour into Search function can save hours or days of waiting for a solution