A minor arc is an arc that measures less than 180.
A major arc is an arc that measures greater than 180.
A semicircle is an arc with endpoints that lie on a diameter.
mKM=160^(∘)
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An arc is a portion of a circle defined by two endpoints. A central angle separates the circle into two arcs — the major arc and the minor arc. These measures of these arcs are related to the measure of the central angle.
Arc
Measure
A minor arc is the shortest arc connecting two endpoints on a circle.
The measure is less than 180 and is equal to the measure of its related central angle.
A major arc is the longest arc connecting two endpoints on a circle.
The measure is greater than 180 and is equal to 360 minus the measure of the minor arc with the same endpoints.
Now, let's consider the given diagram. Note that LN is a diameter and therefore LMN is a semicircle. This means that mLMN=180^(∘)
The arc we are looking at is KM. It is the shortest arc that connects the endpoints K and M. Therefore, KM is a minor arc.
To find it's measure, we will need to use the Arc Addition Postulate. With this postulate and knowing that mLMN=180^(∘) and mMN=120^(∘), we can find mLM.
Arc Addition Postulate
Substitute
Solve
mLM+mMN=mLMN
mLM+120=180
mLM= 60
Let's add the obtained measure to our diagram.
Finally, using the Arc Addition Postulate once more, we can find mKM.
