In an isosceles trapezoid, one of the angles is 20 degrees larger than the other. Find the corners
| April 11, 2021 | education
In an isosceles trapezoid, one of the angles is 20 degrees larger than the other. Find the corners with the smaller base of the trapezoid.
The sum of the angles of the trapezoid at its lateral sides is 180.
Angle BAD + ABC = 180, (1) angle (BCD + ADC) = 180.
Since the angles at the bases of an isosceles trapezoid are equal, the angle ABC = BCD, the angle BAD = ADC.
By condition, the angle (ABC – BAD) = 20, then the angle ABC = BAD + 20.
Substitute in equation 1.
BAD + BAD + 20 = 180.
2 * BAD = 180 – 20 = 160.
Angle BAD = 160/2 = 80.
Angle ABD = 80 + 20 = 100.
Answer: The angles for a smaller base are 100.
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