In an isosceles trapezoid ABCD with bases BC and AD, the diagonal AC is the bisector of the angle BAD.
| July 14, 2021 | education
In an isosceles trapezoid ABCD with bases BC and AD, the diagonal AC is the bisector of the angle BAD. Find the value of the angle АСD in degrees, if you know that the angle АDC = 50 degrees.
Since the trapezoid is isosceles, the angle BAD = CDA = 50.
The diagonal AC, by condition, is the bisector of the angle BAD, then the angle CAD = BAD / 2 = 50/2 = 25.
Consider triangle ACD.
The sum of the inner angles of the triangle is 180, then the angle ACD = 18 – CAD – ADC = 180 – 25 – 50 = 105.
Answer: The angle ACD is 105.
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