When crossing two parallel straight secant lines, one of the corners is 2 times larger than the other, find all the resulting corners.

The secant ТН intersects lines AB and CD at points O and K, respectively. When two parallel cutting lines intersect, 8 angles are formed: 1 – angle AOT, 2 – angle TOB, 3 – angle AOK, 4 – angle KOB, 5 – angle CKO, 6 – angle OKD, 7 – angle CKН, 8 – angle HKD.
1. Angles 1 and 2 are adjacent. Adjacent angles together make up a flat angle, which is 180 degrees. Then:
angle 1 + angle 2 = 180 degrees.
By condition, the angle 1 (x) is 2 times greater than the angle 2 (y):
angle 1 = 2 * angle 2.
We get a system of linear equations:
x + y = 180;
x = 2y.
Substitute the value of the second equation in the first equation instead of x:
2y + y = 180;
3y = 180;
y = 180/3;
y = 60.
x = 2y = 2 * 60 = 120 (degrees).
Angle AOT = 120 degrees, angle TOB = 60 degrees.
2. Angles 1 and 4 are vertical, vertical angles are equal. Then:
angle AOT = angle KOB = 120 degrees;
angle KOB = 120 degrees.
3. Angles 2 and 3 are vertical, vertical angles are equal. Then:
angle TOB = angle AOK = 60 degrees.
Angle AOK = 60 degrees.
4. Angles 2 and 7 – cross-lying, cross-lying angles are equal. Then:
angle TOB = angle CKH = 60 degrees.
Angle CKH = 60 degrees.
5. Angles 6 and 7 are vertical, vertical angles are equal. Then:
angle OKD = angle CKH = 60 degrees.
Angle OKD = 60 degrees.
6. Angles 1 and 8 – cross-lying, cross-lying angles are equal. Then:
angle AOT = angle HKD = 120 degrees.
Angle HKD = 120 degrees.
7. Corners 5 and 8 are vertical, vertical angles are equal. Then:
angle HKD = angle CKO = 120 degrees.
CKO angle = 120 degrees.
Answer: AOT angle = 120 degrees, TOB angle = 60 degrees, AOK angle = 60 degrees, COB angle = 120 degrees, CKO angle = 120 degrees, OKD angle = 60 degrees, CKH angle = 60 degrees, HKD angle = 120 degrees.