Zevoka,
Two fast one using Smart Guides:
A) Just with the paths already there:
1) Drag the blue one by the lowest Anchor Point to snap to that of the green one;
2) With the Rotate Tool, click the coinciding point(s) from one and drag the blue one round it by the lower part of the lower right side down at the green one until you are there and Smart Guides say path, you may also slide along the side until you reach the corner of the green one and Smart Guides say anchor.
B) With an auxiliary line (if larger operating sizes make you feel more comfortable):
0) Direct Select the left slanting side of the green one and Ctrl/Cmd+C+F+X+F to create an independent line, with the bottom left Reference Point chosen in the Transform palette/panel multiply the W by a number (5 or so) and press Ctrl/Cmd+Enter to make it long enough;
1) Drag the blue one by the lowest Anchor Point to snap to that of the green one;
2) With the Rotate Tool, click the coinciding point(s) from one and drag the blue one round it by the upper Anchor Point of the lower right side down until you are there and Smart Guides say path.
