Question

match the conditional statement (p
ightarrow q), the converse (q
ightarrow p), the inverse (sim p
ightarrowsim q), and the contrapositive (sim q
ightarrowsim p) in words. let (p) be \two angles are supplementary\ and let (q) be \the measures of the angles sum to 180(^{circ})\ the conditional statement (p
ightarrow q) the converse (q
ightarrow p) the inverse (sim p
ightarrowsim q) the contrapositive (sim q
ightarrowsim p) :: if the measures of two angles do not sum to 180(^{circ}), then they are not supplementary. :: if the measures of two angles sum to 180(^{circ}), then they are not supplementary. :: if the two angles are not supplementary, then their measures do not sum to 180(^{circ}). :: if the measures of two angles sum to 180(^{circ}), then they are supplementary. :: if two angles are not supplementary, then the measures of the angles sum to 180(^{circ}).

Explanation:

1. For the conditional statement \(p

ightarrow q\), when \(p\) is "two angles are supplementary" and \(q\) is "the measures of the angles sum to 180°", it means if \(p\) is true then \(q\) is true. So it is "If two angles are supplementary, then the measures of the angles sum to 180°".

1. The converse \(q

ightarrow p\) means if \(q\) is true then \(p\) is true. So it is "If the measures of two angles sum to 180°, then they are supplementary".

1. The inverse \(

eg p
ightarrow
eg q\) means if \(p\) is false then \(q\) is false. So it is "If two angles are not supplementary, then their measures do not sum to 180°".

1. The contra - positive \(

eg q
ightarrow
eg p\) means if \(q\) is false then \(p\) is false. So it is "If the measures of two angles do not sum to 180°, then they are not supplementary".

Answer:

• The conditional statement \(p

ightarrow q\): If two angles are supplementary, then the measures of the angles sum to 180°.

• The converse \(q

ightarrow p\): If the measures of two angles sum to 180°, then they are supplementary.

• The inverse \(

eg p
ightarrow
eg q\): If two angles are not supplementary, then their measures do not sum to 180°.

• The contra - positive \(

eg q
ightarrow
eg p\): If the measures of two angles do not sum to 180°, then they are not supplementary.