In a right-angled triangle ABC (angle в = 90), the outer angle at the vertex C is 150

| March 20, 2021 | education

In a right-angled triangle ABC (angle в = 90), the outer angle at the vertex C is 150. Find the value of the angle between the bisector BK and the segment KC

1. The bisector drawn from the vertex B of the triangle divides the right angle ABC into two equal parts, that is, СВK = angle ABK = 90 °: 2 = 45 °.

2. The degree measure of the angle ACB is equal to the difference between the value of the expanded angle (180 °) and the external angle at the vertex C (150 °):

Angle АСВ = 180 ° – 150 = 30 °.

3. Taking into account that the total value of all angles of the triangle is equal to 180 °, we calculate the degree measure of the angle between the bisector ВK and the CК segment (ВKС angle):

ВKС angle = 180 ° – 30 ° – 45 ° = 105 °

Answer: ВKС angle = 105 °.



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