The heights of an isosceles triangle, drawn from the vertices at the base, form an angle of 140
| June 11, 2021 | education
The heights of an isosceles triangle, drawn from the vertices at the base, form an angle of 140 degrees when they intersect. Find the angle opposite the base.
By condition, the angle АМC = 140. Then the angle КМР is equal to the angle АСМ = 140, as are the vertical angles at the intersection of the straight lines CK and AР.
Consider a quadrilateral KMРВ, in which the angles of the ВKM and BPM are straight, since the CK and AР heights, and the angle KMР = 140. Then the angle KВР = 360 – 140 – 90 – 90 = 40.
Answer: The angle opposite the base is 40.
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