The diagonals AC and BD of the trapezoid are the bisectors of the angles BAD and ABC
| July 13, 2021 | education
The diagonals AC and BD of the trapezoid are the bisectors of the angles BAD and ABC, respectively. Angle CBD = 70 Find the angle BAC.
Since BD is the bisector of the angle ABC, then the angle ABD = CBD = 70.
At the trapezoid, the bases are parallel, then the angle ADB = CBD = 70 as criss-crossing angles at the intersection of parallel lines AD and BC secant BD.
In triangle ABD, angle BAD = (180 – ABD – ADB) = (180 – 70 – 70) = 40.
AC, by condition, is the bisector of the angle BAD, then the angle BAC = BAD / 2 = 40/2 = 20.
Answer: The value of the angle BAC is 20.
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