We want to know which of the three rulers are similar. Let's take a look at the given picture.
First, notice that all the rulers are right triangles. This means that we can use what we know about similar triangles to check if any of them are similar. We know that if two angles in a triangle are congruent to two angles in another triangle, then the third angles are also congruent and the triangles are similar. Let's consider the leftmost ruler.
We can see that one of the angles in the leftmost ruler is a right angle with a measure is 90^(∘). The remaining angles have the same measure, x^(∘). Since the measures of the interior angles of a triangle add up to 180^(∘), we can find the value of x! Let's do it!
We found that the value of x is 45. Let's add this information to our picture.
From the picture, we can see that two angles in the leftmost ruler are congruent to two angles in the rightmost ruler. This means that the rulers are similar! Notice that the ruler in the middle has an angle that is not congruent to an angle in either of the other triangles, so it is not similar to other rulers.
