In an isosceles triangle, the height of the triangle was drawn from the top of one corner at the base
| June 14, 2021 | education
In an isosceles triangle, the height of the triangle was drawn from the top of one corner at the base, and the bisector of the triangle from the top of the other corner at the base. One of the angles formed at the intersection of the drawn bisector and the height is equal to 64. Find the angles of this triangle.
By condition, the angle AOK = 64, then the angle COM = AOK = 64 as vertical angles.
The СOM triangle is rectangular, then the angle MCO = (90 – 64) = 26.
CК is the bisector of the angle ACB, then the angle ACB = 2 * MCO = 2 * 26 = 52.
Since the triangle is isosceles, the angle BAC = ACB = 52, then the angle ABC = (180 – 52 – 52) = 76.
Answer: The angles of the triangle are 52.52.76.
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