Step-by-step explanation:
In the usual sense of the term "construct", it is impossible to create a triangle with the given measures. A ruler of some sort must be used in order to make it have the given perimeter. That means you're not doing the construction with a compass and (unmarked) straightedge.
Similarly, it is impossible to "construct" a 55° degree angle. Such an angle can be created using a protractor. (Angles that are multiples of 7.5° can be constructed, but 55° is not one of them.)
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To make the perimeter be 15 units, at least one of the side lengths must be known. The side lengths will be proportional to the sines of the angles, so the scale factor for that can be found as ...
k = 15/(sin(55°) +sin(60°) +sin(65°)) ≈ 15/2.59148 ≈ 5.78819
Then the side opposite the 65° angle, between the 55° and 60° angles, will be ...
k·sin(65°) ≈ 5.24588 . . . . units
With this information, a ruler, and a protractor, the triangle of interest can be created.
(The first attachment is output from a triangle solver showing that the above measurements will result in a triangle with the desired perimeter.)
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The steps could be as follows:
Using a ruler, create line segment AB of length 5.246 units. Using A as its vertex, mark an angle 55° from line AB, and draw its terminal ray. Using B as its vertex, mark an angle 60° from line AB, and draw its terminal ray. The intersection of those rays is point C of the desired triangle ABC. An example is shown in the second attachment.