In an isosceles trapezoid ABCD, where AD and BC are bases, the sum of angles A, B, and C is 290 degrees. Find angle B.
| January 28, 2021 | education
The sum of the inner angles of a trapezoid is 3600.
Then the angle (ABC + ВСD + СDA + DAВ) = 3600.
By condition, the angle ABC + ВСD + DAВ = 2900, then 290 + СDA = 3600.
СDA angle = 360 – 290 = 700.
The sum of the angles at the lateral sides of the trapezoid is 1800, then the ВСD angle = 180 – СDA = 180 – 70 = 1100.
Since the trapezoid is isosceles, then its angles at the bases are equal, then the angle ABC = ВСD = 1100.
Answer: Angle ABC is 1100.
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