Measure the two sides adjacent to the angle and the diagonal at the far ends of these sides. Then use the cosine rule to calculate the angle.
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In general, you will need to use a protractor and measure them.
It is easy to draw an equilateral triangle without a protractor. That gives a 60 degree angle. It is then simply a matter of bisecting the 60 degree angle, using an unmarked rule and compass, to get a 30 degree angle.
One way is to use a protractor. There are others
Using the formula: (number of sides -2)*180 = sum of interior angles
I used a protractor to find the measure of the angle.