You need to use a protractor.
You can also calculate it from the length of the three sides of a triangle it would make. Since an obtuse angle lies between 90 and 180 degrees just draw a line bisecting the two angle lines and measure the length of each of the three resulting sides.
View Wikipedia in the related link below to find out how to use trigonometry to accomplish this.
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The measure of the obtuse angle would then be double that of the acute angle.
An obtuse angle
Obtuse angle (here is the formula) -: 90° = Right angle and if you don't know the obtuse angle is more than 90° so adding 2 will make it an obtuse angle.
Obtuse
Obtuse angle