In a right-angled triangle ABC, the angle C = 90 degrees, the bisectors CM and BK
| February 10, 2021 | education
In a right-angled triangle ABC, the angle C = 90 degrees, the bisectors CM and BK intersect at point O, the angle BOC = 110 degrees. Find an acute angle ABC.
Since CM is the bisector of a right angle, then the angle BCM = 90/2 = 45.
In the ВOС triangle, we determine the value of the OBC angle.
OBC angle = (180 – ВOS – ВСM) = (180 – 110 – 45) = 25.
ВK = bisector of angle ABC, then angle ABC = 2 * OBC = 2 * 25 = 50.
Determine the value of the angle BAC. Angle BAC = (90 – ABC) = (90 – 50) = 40.
Answer: The acute angles of the triangle are 40 and 50.
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