What is the value of Angle BMC in Triangle ABC?

In summary, the value of angle BMC can be found by using the triangle angle sum theorem and knowing the measures of the other angles in the triangle. The triangle angle sum theorem states that the sum of the three angles in any triangle is always 180 degrees. Trigonometry can also be used to find the value of angle BMC if the lengths of the sides of the triangle are known. There is a difference between angle BMC and angle BAC, as they refer to different angles in the same triangle. And finally, a protractor can be used to measure angle BMC if a physical copy or drawing of the triangle is available.
  • #1
Albert1
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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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  • #2
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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Related to What is the value of Angle BMC in Triangle ABC?

1. How do you find the value of angle BMC?

To find the value of angle BMC, you need to know the measures of the other angles in the triangle. You can then use the triangle angle sum theorem, which states that the sum of the three angles in any triangle is 180 degrees, to find the missing angle.

2. What is the triangle angle sum theorem?

The triangle angle sum theorem states that the sum of the three angles in any triangle is always equal to 180 degrees. This theorem is true for all types of triangles: equilateral, isosceles, and scalene.

3. Can you use trigonometry to find the value of angle BMC?

Yes, you can use trigonometry to find the value of angle BMC if you know the lengths of the sides of the triangle. You can use the law of cosines or the law of sines to find the missing angle.

4. What is the difference between angle BMC and angle BAC?

Angle BMC refers to a specific angle in a triangle, namely the angle formed by the lines connecting points B and C to point M. Angle BAC, on the other hand, refers to a different angle in the same triangle, formed by the lines connecting points B and A to point C. These two angles may have different measures.

5. Can you use a protractor to measure angle BMC?

Yes, you can use a protractor to measure angle BMC if you have a physical copy of the triangle or a drawing of it. Simply place the protractor on the lines connecting points B, M, and C and read the measure where the lines intersect on the protractor's scale.

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