In trapezoid ABCD, the diagonal AC bisects angle A and AC = AD. Find the angle D if the angle is BAC = 42 degrees?
| April 22, 2021 | education
According to the condition, AC divides the angle BAD in half, then AC is the bisector, and the angle BAC = CAD = 42.
Also, n condition, the bisector AC is equal in length to the larger base AD, therefore, the triangle ACD is isosceles, then its angles at the base CD are equal, the angle ACD = ADC.
The sum of the angles of a triangle is 180, then:
CAD + ACD + ADC = 180.
42 + 2 * ADC = 180.
ADC = (180 – 42) / 2 = 69.
Answer: Angle D = 69.
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