Find the angle ABC of an isosceles trapezoid ABCD if the diagonal AC forms angles equal to 30 degrees

Find the angle ABC of an isosceles trapezoid ABCD if the diagonal AC forms angles equal to 30 degrees and 80 degrees, respectively, with the base AD and the lateral side CD.

1. Considering that the total value of the inner angles of the AСD triangle is 180 °,

we calculate the degree measure ∠ADС:

∠ADС = 180 ° – ∠СAD – ∠AСD = 180 ° – 30 ° – 80 ° = 70 °.

2. ∠ВAD = ∠ADС = 70 °, since the degree measures of the angles located on the base of the trapezoid are which is isosceles are the same.

3. Considering that the sum of the angles located on the lateral side of the trapezoid (adjacent to it) is 180 °, we calculate the value of ∠АВС:

∠ABС = 180 ° – ∠ВAD = 180 ° – 70 ° = 110 °.

Answer: ∠ABС = 110 °.