Two parallel lines are cut by a transversal. Of the two interior angles on the same side of the transversal, one is 30° less than twice the other. What is the larger of these two angles?

Explanation

1. 01

   Co-interior angles between parallel lines add up to 180°.

2. 02

   Let the smaller be $x$; the larger is $2x - 30$. So $x + 2x - 30 = 180$, giving $x = 70$.

3. 03

   Larger angle = $2 \times 70 - 30 = 110^\circ$.