In triangle ABC, angle A is 78 degrees, and angles B and C are sharp, heights BD and CE meet at point O.
| March 8, 2021 | education
In triangle ABC, angle A is 78 degrees, and angles B and C are sharp, heights BD and CE meet at point O. Find the angle DOE.
Since CE and BD are the heights of the ABC triangle, the angle AEC = AEO = 90, the angle ADB = ADO = 90.
In a convex quadrilateral AEOD, the sum of the interior angles is 360, then the angle DOE = (360 – AEO – ADO – EAD) = (360 – 90 – 90 – 78) = 102.
Answer: The angle DOE is 102.
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