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Use the image to match the arc/angle measure.

(there is one more option that i wasn’t able to get in the photo it is 67°

Use the image to match the arc/angle measure. (there is one more option that i wasn-example-1

1 Answer

4 votes

Answer:

The following measurements are:


m\angle{STR}=23^\circ (Option #4)


m{QT}=142^\circ (Option #7)


mST=134^\circ (Option #5)


mRQ=38^\circ (Option #2)

Explanation:

To begin, we can find the measure of
\angle{STR} by applying the inscribed angle theorem: an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

Since the intercepted arc (RS) is 46 degrees, we have:


46=2\theta\\23=\theta

Next, we can find the measure of arc QT using the same theorem. So,


QT=2(71)\\QT=142

Notice that the chord RT is actually a diameter. From the theorem about the inscribed angle including a diameter, we know that the intercepted arc will have a measure of
180^\circ. Since the arc ST is part of the arc RST, and we know RS is
46^\circ, we can set up and solve this equation:


RST = RS + ST\\180 = 46 + ST\\134 = ST

We can use the same idea to find RQ. We know that RQT is
180^\circ and QT is
142^\circ, so:


RQT = RQ + QT\\180 = RQ + 142\\38 = RQ

User JoKalliauer
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