Question

4) Without a protractor, but with the aid of the two conjectures, find the measure of each lettered angle (see below)

9) You discover that if a pair of angles is a linear pair, then the angles are supplementary. Does that mean that all supplementary angles form a linear pair of angles?

Answer 1

I don't know what your conjectures were, so this may or may not be useful.

Because supplementary angles sum to 180:
65 + d = 65 + f = 180, and d = f = 115
60 + b = 60 + c = 180, so b = c = 120
55 + i = 55 + g = 180, and g = i = 125

Because opposite angles are equal:
a = 60
e = 65

Answer 2

#9 is a simple logical problem, so I will help but not solve it. Imagine a "linear angle" is a "new car", and a "supplementary angle" is "something that you can buy".

Now your sentence reads as follows:
You discover that if an item is a new car, it is something that you can buy. Does that mean all things you can buy are new cars?

I trust this helps. If you dislike the analogy, replace the new car with a cell phone, or a geometry textbook, or an ocean cruise, or whatever you might want to buy.