The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this: 1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal. 2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar. 2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
to make a unit rate using a table you would take an input/output from a table and convert it into a fraction. Then you would take that fraction and simplify it. Sometimes you might have to choose a new input/output in order to make the simplification easier.
These angles should add to 180 degrees because the angles are on a straight line so you should use the formula x=180-90-38. Therefore, x should be 52 degrees
