Co-interior Angles: Identifying α1, β1, α2, β2 with Parallel Lines

Question

Which angles in the drawing are co-interior given that a is parallel to b?

00:00 Determine which of the angles are acute angles

00:03 Corresponding angles occur on the same side and level of the line

00:19 The sum of the acute angles is 180

00:24 The acute angles occur on the same side of the line

00:29 Here is the solution

Given that line a is parallel to line b, the angles $\alpha_2,\beta_1$ are equal according to the definition of corresponding angles.

Also, the angles $\alpha_1,\gamma_1$ are equal according to the definition of corresponding angles.

Now let's remember the definition of collateral angles:

Collateral angles are actually a pair of angles that can be found on the same side of a line when it crosses a pair of parallel lines.

These angles are on opposite levels with respect to the parallel line they belong to.

The sum of a pair of angles on one side is one hundred eighty degrees.

Therefore, since line a is parallel to line b and according to the previous definition: the angles

γ1+γ2=180

are the collateral angles

$\gamma1,\gamma2$