Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: Two angles are supplementary. Conjecture: They are both acute angles.

Question

Jay

Mathematics

10 August, 06:35

Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: Two angles are supplementary. Conjecture: They are both acute angles.

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Answers (1)

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Sherlyn Cooke · Answer 1

This conjecture is false

Explanation:

A Conjecture is only an educated guess which might or might not be true. When two angles are supplementary, it means their sum when added together is 180°. But as per this, conjecture both the angles are acute, which means both are less than 90°. This is not possible.

This can be explained with a counter example. It is an example that can be given to show that a particular conditional statement is false.

If both angles are acute means they are less than 90°. Like one angle is 80° and the other is 70°. Adding 80° and 70° we will get 150°, which is not supplementary.