Hello there. To solve this question using the Law of Detachment, first we need to remember what does this law refers to:
Say we have two propositions p and q.
If p implies q and p is true, q is also true.
For the transitivity property, we'll have:
If p = q and q = r, then p = r.
We want to show that the angles 30º and 60º are complementary using that law.
Remember that two angles are complementary when their sum is equal to a right angle, i. e. 90º.
Most likely, to get to this conclusion, we may need to show that the sum of those terms in different orders, I mean, 30º + 60º = 90º = 60º + 30º won't change the value.
Thus, we'll get two properties in which we'll get to the same conclusion as the first thing marked down in bold.
Let's assume p is equal to the sum of angle 1 and angle 2.
r is the sum of angle 2 and angle 1 (just changed the order)
You can see that p = q, since 30º + 60º = 90º
and q, being the right angle, will also be equal to r, since 90º = 60º + 30º
Thus, p = r, which leads us to the conclusion.
p implies q, p is true and q is also true.
The angles are complementary.
