Suppose the acute angle B has n degrees. True or false: if angle B is subtracted from its supplement the result is twice angle B’s complement.
(a) Give n several values and test this statement.
(b) Show algebraically that the statement is either true or false.
Solution
If you try a few examples, you'll soon believe the statement is true.
Let's try a general argument.
Let S be the supplement of B, and C be the complement.
Then:
S - B = (180 - B) - B = 180 - 2B = 2(90 - B) = 2C.