Question

Is the following statement always, sometimes, or never true? “The supplement of an acute angle is an obtuse angle.” Explain your answer.

Answer 1

The statement is always true because the sum of the two angles must be 180 degrees to be supplementary. If the first angle is an acute angle, then it has a measure of less than 90 degrees. To sum 180 degrees, the second angle would need to be more than 90 degrees, making it an obtuse angle.

Explanation:

Answer 2

YES

Explanation:

The statement “The supplement of an acute angle is an obtuse angle.” is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)