Connect the LED to the voltmeter/multimeter
As with hooking up the LED to the battery, connect the red wire to the long post of the LED and the black wire to the short post.
Turn the voltmeter on and set its sensitivity to 2 volts
Point the LED at a bright light. Align protractor so 90 degrees aligns with the long axis of the LED.
If the voltmeter has a negative reading, reverse the wires to the LED (this does not hurt the voltmeter, but it does make it easier to understand the readings)
Using either a light bulb or a red laser, point the top of the LED toward the light source.
Slowly rotate the LED to see at what point the voltage on the multimeter drops significantly.
Measure this angle for the red LED.
If using a red laser, does the IR LED generate any electrical current? Use an incandescent light to test the IR LED.