Question

question 13
1 pts
read the following conditional statement:
\if two angles add up to 90 degrees, then they are complementary.\
compare each the following options to the original. match the converse, inverse, and contrapositive.
if two angles do not add up to 90 degrees, then they are not complementary.
if two angles are complementary, then they add up to 90 degrees.
if two angles are not complementary, then they do not add up to 90 degrees.

Explanation:

1. For a conditional statement "if p then q", the inverse is "if not p then not q", the converse is "if q then p", and the contrapositive is "if not q then not p". In the given statement "if two angles add up to 90 degrees (p), then they are complementary (q)".
2. "If two angles DO NOT add up to 90 degrees, then they are NOT complementary" is the inverse as it has the form "if not p then not q".
3. "If two angles are complementary, then they add up to 90 degrees" is the converse as it has the form "if q then p".
4. "If two angles are NOT complementary, then they DO NOT add up to 90 degrees" is the contrapositive as it has the form "if not q then not p".

Answer:

• If two angles DO NOT add up to 90 degrees, then they are NOT complementary: Inverse
• If two angles are complementary, then they add up to 90 degrees: Converse
• If two angles are NOT complementary, then they DO NOT add up to 90 degrees: Contrapositive