Question

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

Option: B is the answer.

Explanation:

As we know that an obtuse angle is an angle whose measure is greater than 90° but strictly less than 180°

Now the complement of such a angle could not exist because complement of an angle B is defined as:

A+B=90

A=90-B

now here B has measure >90° so on subtracting this quantity with 90° we will get a negative quantity and measure of any angle can't be negative.

Hence, It is not possible for an obtuse angle to have both a complement and a supplement.

We are asked about the incorrect statement.

Hence option B is the answer.

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

Answer 2

the obtuse angle cannot be a complement
the answer is
B. It is possible for an obtuse angle to have both a complement and a supplement.