To draw △ ABC, use a protractor to construct ∠ C with measure 30^(∘), and a straight edge to draw the sides. On the extension of CA plot any two points. These will be vertices J and L of △ LKJ.
We can guarantee that △ LKJ is similar to △ ABC if the angles are congruent. Let's replicate ∠ C and ∠ A on the vertices J and L. As a first step to replicate ∠ C, draw two arcs with the same compass measure, centered at C and at J.
The arc at △ ABC intersects BC and CA. Use the compass to replicate the distance between the two points of intersection on the other arc.
Use the straightedge to connect the intersection of the two arcs with vertex J. Vertex K will be on this ray.
Note that using this procedure we constructed an angle congruent to ∠ C. Let's repeat the same process to copy ∠ A on vertex L.
Vertex K is the point of intersection of the two rays we have constructed.
Since two angles of △ ABC are congruent to two angles of triangle △ LKJ, by the Angle-Angle Similarity Postulate, the two triangles are similar.
△ ABC~△ LKJ
