Angle A of isosceles trapezoid ABCD is 75 °. From point D. A straight line is drawn
| January 17, 2021 | education
Angle A of isosceles trapezoid ABCD is 75 °. From point D. A straight line is drawn that intersects line BC at point K, and CD = DK. Find angle CDK.
Since, by condition, СD = DC, then DC, in this case, intersects BC on its extension.
The trapezoid of AВСD is isosceles, then the angle of ABС = ВAD = 75.
The sum of the angles of the trapezoid at its lateral side is 180, then the angle of the ВСD = (180 – ADС) = (180 – 75) = 105.
The DSC angle is adjacent to the ВСD angle, then DСК = (180 – 105) = 75.
The SDK triangle is isosceles, since СD = DC, then the angle СDK = DСK = 75.
Then the angle СDK = (180 – 75 – 75) = 30.
Answer: The СDK angle is 30.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
