Start by drawing a circle using the Circle tool, whilst holding down Ctrl
Turn on "Snap to object centre" & "Snap to rotation centre" and create guides that snap to the centre of the circle
With the circle tool and circle still selected, you can calculate the arc length you desire by expressing it as a percentage fraction X 360. i.e. (25/100)*360 can be typed directly into the "End" box to give you 25% arc length which is 90 degrees. Note: the brackets are important.
Make sure you click "Switch to arc" after you calculate the arc size.
With the Selection tool, click the rotation point and move it to the guide intersection. We want to rotate and duplicate the arc around this point.
Clone the arc with Alt+D, and click the arc layer again to make the rotation handles appear. Use the selection tool to rotate the arc around the pivot point, and press SPACEBAR to clone/stamp the arc around this point.
Select all clones and Shift+Alt+D to unlink clones. You can now remove any fills and enter the arc stroke colours as you wish.
For different arc lengths: After you Unlink your arc clones, you can enter different values into the "End" box (whilst the circle tool is selected) for each arc. Make sure you move the centrepoints of the arcs into the intersecting guides & rotate each arc to join them together.