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In the figure below (not to scale), `bar(MR )_|_ bar(MP), bar(MQ) _|_ bar(MN)`, and `bar(MS)` is bisector of `/_ RMQ` . If `/_ PMN=50^(@)` , then find

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In the figure below (not to scale), `bar(MR )_|_ bar(MP), bar(MQ) _|_ bar(MN)`, and `bar(MS)` is bisector of `/_ RMQ` . If `/_ PMN=50^(@)` , then find the measure of `/_ RMS`.
image
A. `25^(@)`
B. `20^(@)`
C. `30^(@)`
D. `35^(@)`
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Correct Answer - a
(i) Find `/_QMP` using `/_ QMP = /_QMN- /_PMN`.
(ii) Find `/_ RMQ ` using `/_ RMQ= 90^(@)- /_ QMP`.
(iii) Now `/_RMS =(1)/(2) /_ RMQ`
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