Question

if parallel lines a and b are cut by transversal t, which pair of angles are same - side interior angles?
options:
∠1 and ∠5
∠3 and ∠6
∠2 and ∠6
∠3 and ∠5

Explanation:

Step1: Recall same - side interior angles definition

Same - side interior angles are two angles that lie between two parallel lines (the interior) and on the same side of the transversal.

Step2: Analyze each option

• Option 1: $\angle1$ and $\angle5$: $\angle1$ is above line $a$ and $\angle5$ is above line $b$. They are corresponding angles, not same - side interior angles.
• Option 2: $\angle3$ and $\angle6$: $\angle3$ is below line $a$ and $\angle6$ is above line $b$. They are alternate interior angles, not same - side interior angles.
• Option 3: $\angle2$ and $\angle6$: $\angle2$ is above line $a$ and $\angle6$ is above line $b$. They are corresponding angles, not same - side interior angles.
• Option 4: $\angle3$ and $\angle5$: $\angle3$ is between line $a$ and line $b$ (interior) and on the left - hand side of transversal $t$, $\angle5$ is between line $a$ and line $b$ (interior) and on the left - hand side of transversal $t$. So they are same - side interior angles.

Answer:

$\angle3$ and $\angle5$ (the last option, i.e., the option with $\angle3$ and $\angle5$)