Question

what is the converse of the following statement?

\if the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle.\

• if the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle.
• if the polygon is a triangle, then the sum of the interior angles of the polygon is not more than 180°.
• if the sum of the interior angles of a polygon is equal to 180°, then the polygon is a triangle.
• if the polygon is not a triangle, then the sum of the interior angles of the polygon is more than 180°.

Explanation:

Identify the hypothesis and conclusion

The original conditional statement is: "If the sum of interior angles of a polygon is more than \(180^\circ\), then the polygon is not a triangle."

• Hypothesis \(p\): "the sum of interior angles of a polygon is more than \(180^\circ\)"
• Conclusion \(q\): "the polygon is not a triangle"

Formulate the converse statement

The converse of a conditional statement "If \(p\), then \(q\)" is "If \(q\), then \(p\)".

• Converse: "If the polygon is not a triangle, then the sum of the interior angles of the polygon is more than \(180^\circ\)."

Match with the given options

Compare the formulated converse statement with the choices:

• Option 1: Inverse statement.
• Option 2: Contrapositive statement (with negation adjusted).
• Option 3: Incorrect variation.
• Option 4: Matches the formulated converse statement exactly.

Answer:

• If the sum of the interior angles of a polygon is not more than \(180^\circ\), then the polygon is a triangle.
• If the polygon is a triangle, then the sum of the interior angles of the polygon is not more than \(180^\circ\).
• If the sum of the interior angles of a polygon is equal to \(180^\circ\), then the polygon is a triangle.
• If the polygon is not a triangle, then the sum of the interior angles of the polygon is more than \(180^\circ\). (Correct answer)