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The needle should form a 15 to 30 degree angle with the surface of the arm.
90 degree angle
Because the goal of the procedure is to place a plastic catheter into the vein. If you insert the needle/catheter vertically you will go through the vein. If you angle on insertion once placement in the vein is confirmed you can slide the hollow catheter off of the needle into the vein. The veins used for most IV's normally lie just under the skin. For this reason a shallow angle of insertion is used.
About a right angle (90 degrees) to the chest, intercostal, into the pleural lining and not into the lung.
30 degrees or less.
90- degree
Inserts a needle at the wrong angle or uses a large-bore needle
3/8
45 degrees
usually the veinipuncture is using a 21 or 22 gauge needle at about a 30 degree or less angle.
15-30 degrees
Would depend on the distance, and the angle of impact. A shot impacting at 90 degrees at close range would be likely to penetrate- a shot at an angle of 45 degrees or greater would be likely to glance off the shield.