Line segment AD – bisector of triangle ABC. A straight line is drawn through point D, parallel to side AB

| August 10, 2021 | education

Line segment AD – bisector of triangle ABC. A straight line is drawn through point D, parallel to side AB and intersecting the side of AC at point K. Calculate the degree measures of the angles of the triangle ADK if the angle BAC = 64 degrees.

1. In geometry it is known that the sum of the angles of a triangle is 180 °.

2. According to the condition of the problem, it is given that in triangle ABC the angle A is equal to 64 °, AD is the bisector of this angle, the segment DK is parallel to the side AB.

3. Since the angle A is divided by the bisector in half, the angle DAC = 64 °: 2 = 32 °.

The angle ADK is equal to the angle BAD as a cross with it with parallel lines AB and DK and secant AD, that is, the angle ADK = 64 °: 2 = 32 °.

Angle AKD = 180 ° – 32 ° – 32 ° = 116 °.

Answer: In triangle ADK, angles DAK and ADK are 32 °, angle AKD = 116 °.



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