Find The marked angle below.

The two horizontal lines are parallel. The slanted line that passes through $t, y, s, \omega$ is a transversal. The other slanted line that forms the $30^\circ$ angle is a separate transversal.

The angle marked $70^\circ$ and angle $t$ are angles on a straight line (linear pair) with respect to the top parallel line and the right transversal. They are also consecutive interior angles if we consider the transversal and the top parallel line.
The $70^\circ$ angle is an alternate interior angle to the angle below the top parallel line, on the left side of the transversal.
The $70^\circ$ angle and angle $t$ are supplementary angles because they form a linear pair along the transversal.

Since the two horizontal lines are parallel, we can use properties of parallel lines and transversals.
Angle $t$ and angle $y$ are consecutive interior angles. Therefore, they are supplementary.

Angle $s$ and angle $y$ are vertically opposite angles. Therefore, they are equal.

Angle $\omega$ and angle $t$ are alternate exterior angles. Therefore, they are equal.

Alternatively, angle $\omega$ and angle $y$ are angles on a straight line (linear pair).

The $30^\circ$ angle is not used to find $t, y, s, \omega$ as it is formed by a different transversal. If it were part of the same transversal, the problem would be different. Based on the drawing, it's an angle formed by a separate line.

The marked angles are:

• $t = \boxed{\text{110}^\circ}$
• $y = \boxed{\text{70}^\circ}$
• $s = \boxed{\text{70}^\circ}$
• $\omega = \boxed{\text{110}^\circ}$