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Prove: If two angles are supplementary, they also form a linear pair.

Which image provides the best counterexample for this statement?

Prove: If two angles are supplementary, they also form a linear pair. Which image-example-1
User MoiioM
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2 Answers

26 votes
26 votes

The statement "If two angles are supplementary, they also form a linear pair" is true. Image B provides a counterexample to this statement. Therefore ,Image B is correct .

Two angles are supplementary if their measures add up to 180 degrees. A linear pair is two adjacent angles that together form a straight angle (180 degrees).

To prove that if two angles are supplementary, they also form a linear pair, we need to show that they are adjacent.

Let A and B be two supplementary angles.

This means that their measures add up to 180 degrees:

m(A) + m(B) = 180 degrees

In the diagram, we see that angles A and B are adjacent.

This is because they share a common vertex (point O) and a common side (ray OB).

Therefore, if two angles are supplementary, they also form a linear pair.

Counterexample:

Image B is the best counterexample for the statement "If two angles are supplementary, they also form a linear pair."

The angles in Image B are supplementary (they add up to 180 degrees), but they do not form a linear pair.

This is because they are not adjacent. They do not share a common side.

Therefore, Image B is the best counterexample for the statement.

User Deesbek
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Based on the definition of supplementary angles and linear pair, a counterexample to the statement is: option B.

What are Supplementary Angles?

If two angles add up to give 180 degrees, they are regarded as supplementary angles.

What is a Linear Pair?

A linear pair is two adjacent angles that share a common side on a straight line, and have a sum of 180 degrees. Linear pair angles are supplementary angles.

In the image given, figure D is a perfect example of a linear pair that are supplementary.

However, in figure B, we have two angles that are not adjacent angles on a straight line but are supplementary angles.

Therefore, a counterexample to the statement is: option B.

Learn more about supplementary angles on:

User Zonble
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