What is the value of Angle BMC in Triangle ABC?

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SUMMARY

The value of angle BMC in triangle ABC, where angle BAC and angle ACB are both 50 degrees, can be calculated using the given angles at point M. With angle MAC at 10 degrees and angle MCA at 30 degrees, angle BMC is determined to be 100 degrees. This conclusion is reached by applying the properties of triangle angles and the sum of angles in a triangle.

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$\triangle ABC ,if \,\, \angle BAC=\angle ACB=50^o$

point $M$ is an inner point of $\triangle ABC ,$

given :$\angle MAC=10^o$ and $\angle MCA=30^o$

find the value of $\angle BMC=?$
 
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Albert said:
$\triangle ABC ,if \,\, \angle BAC=\angle ACB=50^o$

point $M$ is an inner point of $\triangle ABC ,$

given :$\angle MAC=10^o$ and $\angle MCA=30^o$

find the value of $\angle BMC=?$
my solution:
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