Question

Tell whether the reasoning process is deductive or inductive.

Look at the discussion leading up to the statement of Theorem 3-13 on page 102. Is the thinking inductive or deductive?

Short answer

The reasoning process isinductive.

Step-by-step solution

Step 1. Define deductive reasoning.

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Step 2. Define inductive reasoning.

Inductive reasoning is conclusions based on several past observations.

Step 3. State whether the reasoning is inductive or deductive.

From the given statement, note that Theorem 3-13 states, “the sum of the measures of the angles of a convex polygon with n sides is $\left(n-2\right)180°$.”.

The reasoning in the given theorem uses several previous observations. According to the above definition if any conclusion is based on several past observations, then it is called inductive in nature.

Hence, the given statement is inductive in nature.