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How to Construct an Acute Triangle. To construct an acute triangle, simple first construct an angle that is less than 90 degrees and greater than 0 degrees. This will create two sides of your triangle. Then cnstruct a third line intersecting your first two, and you have an acute triangle.
You probably know that the sum of any triangle's angles is always 180 degrees. In an acute triangle, the sum of any two angles is always greater than 90 degrees. This is because in an acute triangle, no one angle can be greater than 89.999 degrees (and yes, those nines could go on forever). So the other two angles must add up to at least 180 minus 89.999 (or 90.001) degrees.