a. 

m1, m2, and m3 add up to 180° because they lie on a straight line.

b. 

1 is the same as 5 because they are corresponding angles.

c. 

2 is the same as 6 because they are vertical angles.

d. 

3 is the same as 4 since they are corresponding angles.

e. 

Since m1, m2, and m3 add up to 180°, and because they respectively equal 5, 6, and 4, it follows that m4, m5, and m6 add up to 180°. Since the reasoning that led us to the conclusion did not use any specific angle measure in the given picture, it holds in general. Note that this is a proof that shows there are 180° in every triangle!

a. 

The measure is 90° (or 360° / 4).

b. 

The measure is 180° (or 360° / 2).

c. 

The measure is 120° (or 360° / 3).

d. 

If a central angle cuts off an arc of one n-th of the full circle, its measure is
360° / n.

a. 

The central angle is larger.

b. 

It is twice as large.

c. 

Answers will vary. One way to answer the question is to use the software to sketch the figure, then measure the two angles. If you tested this for several cases, it would lead to a conjecture that can be made here: Angles inscribed in circles have measures that are half the measure of the arc they intercept (cut off), which is equivalent to the measure of the central angle. Try it.