Two parallel lines are cut by a transversal as shown below. Suppose m 2 7 = 103°. Find m Z 2 and m 2 4.
m2 2 =
x
?
1/2
5/6
8/7
4/3
m2 4 = 1
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Asoccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.1 in

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Points a, b, and c form a triangle. complete the statements to prove that the sum of the interior angles of triangle abc is 180