Question

1. two complementary angles form a linear pair. 23. the supplement of an obtuse angle is an acute angle. 24. an angle that has a supplement also has a complement. tell whether the statement is always, sometimes, or never true.

Explanation:

Step1: Recall angle - pair definitions

Complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees.

Step2: Analyze statement 22

Complementary angles sum to 90 degrees. A linear - pair sums to 180 degrees. So two complementary angles never form a linear pair.

Step3: Analyze statement 23

An obtuse angle is greater than 90 degrees. Its supplement is 180 degrees minus the obtuse - angle measure, which is less than 90 degrees (an acute angle). So the supplement of an obtuse angle is always an acute angle.

Step4: Analyze statement 24

Let the angle be \(x\). Its supplement is \(180 - x\) and its complement is \(90 - x\). If an angle has a supplement (\(180 - x>0\)), for it to have a complement \(90 - x>0\). But if \(x\geq90\), it has a supplement but no complement. So an angle that has a supplement does not always have a complement.

Answer:

1. Never true
2. Always true
3. Sometimes true