Question

1. fill in the blanks to complete the alternate form of the statement. say whether it is true or false. \if two angles are a linear pair, then the angles add to 180 degrees.\ inverse: if two angles \\(\square\\), then the angles \\(\square\\). true or false: \\(\square\\) 11. fill in the blanks to complete the alternate form of the statement. say whether it is true or false. \if two angles are a linear pair, then the angles add to 180 degrees.\ contrapositive: if two angles \\(\square\\), then the angles \\(\square\\). true or false \\(\square\\)

Explanation:

Question 10 (Inverse of the statement)

Step 1: Recall the definition of inverse

The inverse of a conditional statement "If \(p\), then \(q\)" is "If \(
eg p\), then \(
eg q\)". Here, \(p\): "two angles are a linear pair", \(q\): "the angles add to 180 degrees". So \(
eg p\) is "two angles are not a linear pair" and \(
eg q\) is "the angles do not add to 180 degrees".

Step 2: Determine truth value

Two angles that are supplementary (add to \(180^\circ\)) but not a linear pair (e.g., two angles in a parallelogram that are adjacent but not a linear pair? Wait, no—e.g., two angles formed by two intersecting lines but not adjacent? Wait, actually, two angles can add to \(180^\circ\) without being a linear pair (e.g., two angles separated by a transversal, like same - side interior angles in parallel lines). So the inverse is false because there exist angles that are not a linear pair but still add to \(180^\circ\).

Question 11 (Contrapositive of the statement)

Step 1: Recall the definition of contrapositive

The contrapositive of a conditional statement "If \(p\), then \(q\)" is "If \(
eg q\), then \(
eg p\)". Here, \(p\): "two angles are a linear pair", \(q\): "the angles add to 180 degrees". So \(
eg q\) is "two angles do not add to 180 degrees" and \(
eg p\) is "two angles are not a linear pair".

Step 2: Determine truth value

By the definition of a linear pair, a linear pair of angles must be adjacent and supplementary (add to \(180^\circ\)). So if two angles do not add to \(180^\circ\), they cannot be a linear pair (since a linear pair requires them to add to \(180^\circ\)). Thus, the contrapositive is true.

Answer:

Inverse: If two angles \(\boldsymbol{\text{are not a linear pair}}\), then the angles \(\boldsymbol{\text{do not add to 180 degrees}}\).
True or False: \(\boldsymbol{\text{False}}\)