The Arc Addition Postulate tells us that the measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.
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Practice makes perfect
In the given diagram, we want to find the measure of the arc RT.
Note that the minor arc RS and the minor arc QR are adjacent arcs. By the Arc Addition Postulate, we know that the measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs. In this case, the arc formed by these two adjacent arcs is a full semicircle, which measures 180.
145 +mRS=180 ⇔ mRS=35
Finally, we can find the measure of the arc RT using the Arc Addition Postulate one more time. Since we know that mRS=35 and mST=86, we can write the equation for mRT and substitute these values to solve it.
