Final answer:
The converse of the given conditional statement is "If an angle measures between (but not including) 90° and 180°, then it is obtuse," where the hypothesis and conclusion are reversed from the original statement.
Step-by-step explanation:
The converse of the conditional statement "An angle is obtuse when it measures between (but not including) 90° and 180°" is "If an angle measures between (but not including) 90° and 180°, then it is obtuse." To construct the converse of a conditional statement, you simply reverse the hypothesis and the conclusion. The original statement has the form "If P, then Q", where P is "an angle measures between 90° and 180°" and Q is "the angle is obtuse". Therefore, the converse - "If Q, then P" - tells us that if an angle is known to be obtuse, then its measure must fall between 90° and 180°, not including these endpoints.