One of the inner one-sided angles with parallel straight lines and a secant is 17 times

One of the inner one-sided angles with parallel straight lines and a secant is 17 times smaller than the other, find the smaller of these angles?

1. AOD is 17 times less than AOC. Therefore, ∠AOC = 17∠AOD.

2. For calculations, we use the property of internal one-sided angles that their total value is 180 °:

AOD + ∠AOC = 180 °. We substitute 17∠АD in this expression instead of АОС:

AOD + 17∠ AOD = 180 °.

18∠АD = 180 °.

∠AOD = 180 °: 18 = 10 °.

AOC = AOD x 17 = 10 x 17 = 170 °.

Answer: ∠АОD = 10 ° – the smaller of the given angles.