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allochka39001 [22]
3 years ago
13

Given: circle k(O), m LM = 164°, m WK = 68°, m∠MLK = 65°. Find: m∠LMW

Mathematics
1 answer:
Musya8 [376]3 years ago
4 0

Answer:

The measure of angle LMW is m\angle LMW=67\°

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc MW

we know that

The inscribed angle measures half that of the arc comprising

so

m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK]

substitute the given values

65\°=\frac{1}{2}[arc\ MW+68\°]

130\°=[arc\ MW+68\°]

arc\ MW=130\°-68\°=62\°

step 2

Find the measure of arc LK

we know that

arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\° -----> by complete circle

substitute the given values

164\°+62\°+68\°+arc\ LK=360\°

294\°+arc\ LK=360\°

arc\ LK=360\°-294\°=66\°

step 3

Find the measure of angle LMW

we know that

The inscribed angle measures half that of the arc comprising

so

m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK]

substitute the given values

m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°

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