Very simply put, a conjecture is a hypothesis or an educated guess. It is usually based on pattern of examples or non-examples.

Look at the information given below.

These are examples of willow angles.

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1. It takes 2 adjacent angles to make a willow angle.
2. The sum of the angles of a willow angle is 60°.

Now let's look at some angles that are NOT willow angles.

These are NOT willow angles.

Observation 1: It takes 2 adjacent angles to make a willow angle.

This is still true, since the first diagram that is NOT an example of willow angles has 3 angles.

Observation 2: The sum of the angles of willow angles is 60°.

This is still true since the second diagram shows 2 adjacent angles whose sum is 50°.

So, what conjecture could we make about willow angles?

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Willow angles are 2 adjacent angles whose sum is 60°.

Look at the following examples and non-examples of jory angles.

 m∠1 = 45° m∠1 = 50° m∠2 = 20° m∠2 = 50° m∠3 = 35° These are NOT jory angles. These are jory angles. m∠1 = 40° m∠1 = 30° m∠2 = 40° m∠2 = 25° m∠3 = 20° m∠3 = 20° These are jory angles. These are NOT jory angles.