In trapezoid ABCD AB = CD, AC = AD and angle ABC = 117. Find angle CAD.
August 27, 2021 | education|
For a trapezoid, the sum of the angles at the sides is 180.
Angle ABC + BAD = 180. Then angle BAD = 180 – 117 = 63.
Since, by condition, AB = CD, the trapezoid is isosceles, and therefore the angle ADC = BAD = 63.
Consider a triangle ACD, which, by condition, has a segment AC = AD, then the triangle is isosceles and the angle ACD = ADC = 63.
Then the value of the angle CAD = 180 – 63 – 63 = 54.
Answer: Angle CAD = 54.
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