Name the shaded angle in three different ways 3. LKM JKL JKM 2 MKJ K K 2 M L
The Correct Answer and Explanation is:
Here are the three correct ways to name the shaded angle from the list of options:
- JKM
- 2
- MKJ
Explanation
In geometry, it is crucial to name angles with precision to avoid confusion. There are several accepted conventions for naming an angle. Let’s explore these methods using the provided diagram to identify the three correct names for the shaded angle.
1. Naming an Angle with Three Points
The most common and descriptive way to name an angle is by using three points. The rule is as follows:
- The middle letter must always be the vertex of the angle (the point where the two rays meet).
- The other two letters are points on each of the two rays that form the angle. The order of these outer letters does not matter.
In the given figure, the shaded angle has its vertex at point K. The two rays that form this angle pass through points J and M. Therefore, we can name the angle by placing the vertex, K, in the middle. This gives us two possible names:
- ∠JKM (starting from point J, to the vertex K, then to point M)
- ∠MKJ (starting from point M, to the vertex K, then to point J)
Both JKM and MKJ are correct ways to name the shaded angle.
2. Naming an Angle with a Number
Sometimes, for clarity, an angle is labeled with a number placed inside the arc of the angle. This is a simple and unambiguous way to refer to a specific angle, especially in complex diagrams with many angles.
In the diagram, the shaded angle is clearly marked with the number 2. Therefore, another correct way to identify this angle is simply as ∠2.
3. Naming an Angle with the Vertex (and When Not To)
An angle can sometimes be named using only the single letter of its vertex. However, this method is only acceptable when there is only one angle associated with that vertex.
In our diagram, vertex K is the vertex for three different angles: ∠JKM (the shaded angle), ∠MKL (the adjacent angle), and ∠JKL (the large angle combining the other two). Because naming the angle “∠K” would be ambiguous, it is not a correct way to identify the shaded angle in this context.
