Question

Найтите угол АВС равнобедренной трапеции АВСD,если диагональ АС образует с основанием АD и боковой стороной СD углы,равные 30° и 80° соответственно

Answer 1

Угол АВС=180-(30+80)=70

Answer 2

Finding the Angle ABC of an Isosceles Trapezoid ABCD

To find the angle ABC of the isosceles trapezoid ABCD, we need to use the given information that the diagonal AC forms angles of 30° and 80° with the base AD and the side CD, respectively.

Let's break down the problem step by step:

1. Identify the given angles: - Angle CAD = 30° - Angle ACD = 80°

2. Use the properties of isosceles trapezoids: - In an isosceles trapezoid, the base angles (angles formed by the bases and the non-parallel sides) are congruent. - Therefore, angle ABC = angle BCD.

3. Find angle BCD: - Since angle ACD is given as 80°, and angle ABC = angle BCD, we can conclude that angle BCD is also 80°.

4. Find angle ABC: - Since angle ABC = angle BCD, and angle BCD is 80°, we can conclude that angle ABC is also 80°.

Therefore, the angle ABC of the isosceles trapezoid ABCD is 80°.

Please let me know if you need any further assistance!