Let's analyze the image and solve the problem step by step.

We are given that $\angle 5 = 55^\circ$, and we need to determine the measure of $\angle 3$.

Looking at the diagram:

1. Lines $a$ and $b$ are parallel, and line $t$ is a transversal.
2. $\angle 5$ and $\angle 3$ are alternate interior angles because they lie on opposite sides of the transversal $t$, and between the two parallel lines $a$ and $b$.

For alternate interior angles, the rule is that they have the same measure if the lines are parallel. Since lines $a$ and $b$ are parallel, we can conclude that:

$\angle 3 = \angle 5 = 55^\circ$

Thus, the correct answer is:

• 55° because alternate interior angles have the same measure.

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. What are corresponding angles in parallel lines cut by a transversal?
2. How do you prove two angles are supplementary?
3. Can you explain the concept of vertically opposite angles?
4. What is the sum of the interior angles in any triangle?
5. How do you calculate the exterior angle of a polygon?

Tip: Remember that alternate interior angles are always congruent when two parallel lines are cut by a transversal.