Solve the following geometry problems involving parallel lines and transversals, expressing relationships between angles: a) Given angles A4 = a and B1 = 6p, find the equation relating a and p. b) Giv

Lines CD and EF are parallel, indicated by the arrows on the lines. Line GH is the transversal intersecting these parallel lines.

Angle $A_4$ is labeled as $a$. This is the bottom-left interior angle at intersection A.
Angle $B_1$ is labeled as $6p$. This is the top-left interior angle at intersection B.

When two parallel lines are intersected by a transversal, consecutive interior angles (angles on the same side of the transversal and between the parallel lines) are supplementary, meaning they add up to $180^\circ$. Angles $A_4$ and $B_1$ are consecutive interior angles.

Therefore, we have:

Substituting the given expressions:

Lines CD and EF are parallel, indicated by the arrows on the lines. Line GH is the transversal intersecting these parallel lines.

Angle $A_2$ is marked with a square symbol, which indicates a right angle. So, $A_2 = 90^\circ$. This is the top-right angle at intersection A.
Angle $B_2$ is labeled as $a$. This is the top-right angle at intersection B.

When two parallel lines are intersected by a transversal, corresponding angles (angles in the same relative position at each intersection) are equal. Angles $A_2$ and $B_2$ are corresponding angles.

Therefore, we have:

Substituting the given value: