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

August 23, 2021 | education

| **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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