An angle ABC is given equal to 68 degrees. Through point D, lying on its bisector, a straight line is drawn parallel to line BC
| June 1, 2021 | education
An angle ABC is given equal to 68 degrees. Through point D, lying on its bisector, a straight line is drawn parallel to line BC and intersecting the side AB at point E. Find all the angles of the triangle BDE.
Since BD is the bisector of the angle ABC, then the angle EBD = CBD = 68/2 = 34.
By condition, ED is parallel to BC, then the angle EDB = CBD = 34 as criss-crossing angles at the intersection of parallel lines ED and BC of the secant BD. Then the angle CED = (180 – 34 – 34) = 112.
Answer: The angles of the triangle BDE are 34.34, 112.
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