Question

HELP I WILL FAN AND MEDAL

Which of the following statements about special angle relationships is not correct?

A. It is possible for angles to be both vertical and complementary.

B. It is possible for an obtuse angle to have both a complement and a supplement.

C. It is possible for an acute angle to have both a complement and a supplement.

D. It is possible for angles to be both congruent and supplementary

Answer 1

B.) It is possible for an obtuse angle to have both a complement and a supplement.

Step-by-step explanation:

Rules for an obtuse angle:

• It cannot be smaller than or be 90°

• It can not be bigger than or be 180°

To create a complementary or supplementary angle, you can use 2 angles and no more than 2.

Say we used an obtuse angle (like the one in the picture below), since an obtuse angle can not be or be greater than 90°, an obtuse angle can not be complementary.

We can not fit 2 obtuse angles at 180°, because of that, an obtuse angle(s) can not create a supplementary angle.

Therefore, B would be the correct answer.

-kiniwih426

Answer 2

Answer:
Second choice: It is possible for an obtuse angle to have both a complement and a supplement.

Step-by-step explanation:
Let's examine the given choices:

First choice:
It is possible for angles to be both vertical and complementary.
Vertical angles are equal angles.
Complementary angles means that the two angles add up to 90 degrees.
Two angles can be both vertical and complementary if the measure of each is 45. By this, the two angles are equal and their summation is 90 degrees.
Therefore, this statement is correct

Second choice:
It is possible for an obtuse angle to have both a complement and a supplement.
Complement angles means that their sum is 90 degrees.
Supplement angles means that their sum is 180 degrees.
Since the measure of an obtuse angle is greater than 90, therefore, it cannot have a complement.
Therefore, this statement is not correct

Third choice:
It is possible for an acute angle to have both a complement and a supplement.
Complement angles means that their sum is 90 degrees.
Supplement angles means that their sum is 180 degrees.
Since the measure of an acute angle is less than 90, therefore, it can have both a complement and a supplement.
Therefore, this statement is correct

Fourth choice:
It is possible for angles to be both congruent and supplementary
Congruent angles means that they are equal
Supplement angles means that they add up to 180 degrees.
Two angles can be both congruent and supplement if the measure of each is 90. By this, the two angles are equal and their summation is 180 degrees.
Therefore, this statement is correct

Based on the above, the only incorrect statement is the second choice.

Hope this helps :)