In an isosceles triangle ABC, the angle B is 110. Inside the triangle, point M is taken so MCA = 25. Find the angle BMC.
| June 21, 2021 | education
Since the triangle ABC is isosceles, its angles at the base of the AC are equal.
Angle BAC = BCA = (180 – ABC) / 2 = (180 – 110) / 2 = 70/2 = 35.
The height ВD in an isosceles triangle is also its bisector, then the angle CBM = 110/2 = 55. In the triangle CBM, the angle ВСМ = ВСD – DCМ = 35 – 25 = 10.
Then the angle BMC = (180 – CBM – BCM) = (180 – 55 – 10) = 115.
Answer: The naval angle is 115.
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