# The height of a triangle divides the angle of the vertex of which it is dropped by two angles

The height of a triangle divides the angle of the vertex of which it is dropped by two angles containing 30 degrees and 40 degrees to find all the corners of one triangle.

Since the height is a perpendicular to the side, the angle AHB = CHB = 90.

In triangle ABH, by condition, angle ABH = 40, then angle BAH = BAC = 180 – 90 – 40 = 50.

In the CBH triangle, by condition, the angle CBH = 30, then the angle BCH = BCA = 180 – 90 – 30 = 60.

Determine the value of the angle ABC. Angle ABC = ABH + CBH = 40 + 30 = 70.

Check: ABC + BCA + BAC = 70 + 60 + 50 = 180.

Answer: The angles of the triangle are equal: 50, 60, 70.

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