The image contains two geometrical figures and related questions on angles formed by parallel lines and transversals.

Let's solve the relevant parts:

Question 3:

In the given figure, if ∠1 = 30°, find ∠2 and ∠3.

Solution:

• Since lines are parallel and a transversal cuts through them, corresponding angles are equal.
• ∠1 and ∠3 are corresponding angles, so ∠3 = 30°.
• ∠1 and ∠2 are supplementary (they form a straight line), so ∠2 = 180° - 30° = 150°.

Therefore:

• ∠2 = 150°
• ∠3 = 30°

Question 4:

Given that p || q and l || m, find the marked angles in the figure.

Figure (b):

The figure shows two parallel lines p and q, with a transversal line cutting through them, forming a series of angles.

• The marked angle is 85°.

By using the property of corresponding angles and vertically opposite angles:

• x is a corresponding angle to 85°, so x = 85°.

Therefore, the value of the marked angle is:

• x = 85°

Would you like further clarification or more detailed steps?

5 Related Questions:

1. What is the property of alternate interior angles in parallel lines?
2. How are vertically opposite angles related to each other?
3. Can you explain what makes two angles supplementary?
4. How do we identify corresponding angles when two parallel lines are cut by a transversal?
5. How does the sum of interior angles on the same side of a transversal relate to parallel lines?

Tip:

When working with parallel lines and a transversal, always look for corresponding, alternate interior, or supplementary angles to solve for unknown values efficiently.