Complementary and Supplementary Angles?

Question

I know that a complementary angle is 90 and a Supplementary is 180 but in the following questions Im not sure how to apply that to get an answer.

Determine whether the statement is ALWAYS,SOMETIMES, or NEVER true.

1.) If two angles are complematary they are both acute angles.

Im not sure if it means both angles combined or separate to be acute.

2.) If lines PN and PQ are perpendicular then angle NPQ is acute

Answer 1

1) always true--two angles added together to equal 90 degrees must both be under 90 degrees each, or acute
2) never true--two perpendicular lines equal 90 degrees, not acute

Answer 2

If two angles are complementary then they must be acute since neither angle can be greater then 90 degrees. In the the second question, angle npq is a right angle.

Answer 3

1) The answer would be ALWAYS since complementary angles are angles whose sum of their measures is 90. That means that the angles should not be equal or exceed 90. If each should be less than 90 then it is always acute.

(I think you mistaken complementary "angles" to right angles because you use the singular form. Complementary angles are always paired.)

2) The answer would be NEVER because according to the definition of perpendicular segments, perpendicular segments are segments that intersect to form RIGHT ANGLES.

Answer 4

Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. So, 1) always, add the angles together; 2) never. the lines are perpendicular, so these particular line segments define a right angle.

Answer 5

1) sometimes
0+90=90 not acute angles
40+50=90 acute angles

2) never

Answer 6

1.yes.true
2.no,it will be a right angle