In an isosceles triangle ABC with base AC, the heights AD and BE meet at an angle of 50 degrees.
| September 14, 2021 | education
In an isosceles triangle ABC with base AC, the heights AD and BE meet at an angle of 50 degrees. Find the angles of this triangle.
The angles BOD and EOD are adjacent, then the angle EOD = (180 – 50) = 130.
In a quadrangle ODCE, the angle ODCE = OEC = 90, then the angle DCE = ACB = (360 – 90 – 90 – 130) = 50.
Since the triangle ABC is isosceles, then the angle BAC = ACB = 50, then the angle ABC = 180 – 50 – 50 = 80.
Answer: The angles of the triangle are 50, 50, 80.
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