Conjecture About Angles

Acute angle B has n degrees. Consider this statement: “If angle B is subtracted from its supplement, then the result is twice the complement of angle B.”

  1. Give n several values, then see whether you think the sentence is true.
  2. Show algebraically that the statement is true or not true.

Show/Hide 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.

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