Let's consider each of the statements one at a time using the given

p

and

q .

p = q = Two angles are supplementary The measures of the angles sum to 18 0^{\circ}

We can write the conditional statement,

p \to q,

in an if-then form.

If a n a n g l e m e a s u r e i s 16 7^{\circ}, then t h e a n g l e i s o b t u s e .

By the definition of obtuse angles we know that they are between

9 0^{\circ}

and

18 0^{\circ},

which means this is true.

The converse of a conditional statement,

q \to p,

exchanges the hypothesis and the conclusion of the conditional statement.

If a n a n g l e i s o b t u s e, then t h e a n g l e m e a s u r e i s 16 7^{\circ} .

This is not a true statement, as an obtuse angle can have a different measure than

16 7^{\circ} .

The inverse of a conditional statement,

\sim p \to \sim q,

requires us to negate the hypothesis and the conclusion of the conditional statement.

If a n a n g l e m e a s u r e i s not 16 7^{\circ}, then t h e a n g l e i s not o b t u s e .

Again, this is not a true statement, as an obtuse angle can have a different measure than

16 7^{\circ} .

The contrapositive of a conditional statement,

\sim q \to \sim p,

starts out with the converse of the conditional statement. Then we have to negate the hypothesis and the conclusion.

If a n a n g l e i s not o b t u s e, then t h e a n g l e m e a s u r e i s not 16 7^{\circ} .

This is true, since an angle that is not obtuse cannot have an angle measure that is in the interval

90 \leq v \leq 18 0^{\circ} .

Exercise