d The measure of a major arc is the difference of 360^(∘) and the measure of the related minor arc.
A
a 132^(∘)
B
b 147^(∘)
C
c 200^(∘)
D
d 160^(∘)
Practice makes perfect
a We are asked to determine the measure of arc JL. Since the arc is described only with the endpoints J and L, it is a minor arc. Let's highlight JL on the given diagram.
We can see that JL consists of two adjacent arcs JK and KL. Therefore, we will use the Arc Addition Postulate to find mJL.
mJL=mJK+mKL
From the diagram we have that mJK=53^(∘) and mKL=79^(∘). Let's substitute these values into the above equation and evaluate.
b We are asked to determine the measure of arc KM. Since the arc is described only with the endpoints K and M, it is a minor arc. Let's highlight KM on the given diagram.
We can see that KM consists of two adjacent arcs KL and LM. Therefore, we will use the Arc Addition Postulate to find mKM.
mKM=mKL+mLM
From the diagram we have that mKL=79^(∘) and mLM=68^(∘). Let's substitute these values into the above equation and evaluate.
c We are asked to determine the measure of arc JLM. Since the arc is described with the endpoints J and M and a point on the arc L, it is a major arc. Let's highlight JLM on the given diagram.
We can see that JLM consists of three arcs JK, KL, and LM. Therefore, we will use the Arc Addition Postulate to find mJLM.
mJLM=mJK+mKL+mLM
From the diagram we have that mJK= 53^(∘), mKL= 79^(∘), and mLM= 68^(∘). Let's substitute these values into the above equation and evaluate.
d We are asked to determine the measure of arc JM. Since the arc is described only with the endpoints J and M, it is a minor arc. Let's highlight JM on the given diagram.
To find the measure of JM, we will use the fact that the measure of a major arc with the same endpoints J and M is 360^(∘) minus the measure of JM.
mJLM=360^(∘)-mJM
Recall that in Part C we have determined that mJLM=200^(∘). Now we can find the value of mJM.
