A protractor is a tool that may be used to measure an angle. The measure of the angle exists irrespective of the tool that is used to measure it. In the same way that you have a height and your height is a [mainly] fixed amount and whether it is measured with a rule or a tape measure or a laser range finder does not affect your height!
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By using a protractor or using trigonometry
When measuring an angle you have to measure the sides using a protractor.
Place the center point of the protractor at the vertex of the angle and one of the lines of the angle along the zero line of the protractor. The measure of the angle will then be where on the protractor's angular scale the other line of the angle lies.
With the information given in the question, the only answer that I can offer is that you measure it, using a protractor.
A protractor can be used to measure an angle.