Question

which is the contrapositive of this statement? \if the shape is a triangle, then the sum of the angles is 180 degrees.\ if the sum of the angles is 180 degrees, then the shape is a triangle. if the shape is not a triangle, then the sum of the angles is not 180 degrees. if the sum of the angles is not 180 degrees, then the shape is not a triangle. the shape is a triangle if and only if the sum is 180 degrees.

Explanation:

Step1: Recall the definition of contrapositive

The contrapositive of a statement “If \(p\), then \(q\)” (\(p
ightarrow q\)) is “If not \(q\), then not \(p\)” (\(
eg q
ightarrow
eg p\)).
Let \(p\) be “the shape is a triangle” and \(q\) be “the sum of the angles is 180 degrees”.

Step2: Apply the contrapositive rule

The original statement is \(p
ightarrow q\). Its contrapositive is \(
eg q
ightarrow
eg p\).
Substituting the values of \(p\) and \(q\), we get “If the sum of the angles is not 180 degrees, then the shape is not a triangle”.

Answer:

If the sum of the angles is not 180 degrees, then the shape is not a triangle.