Let's go over the problems step by step from the image you've uploaded. I'll explain the approach to solving each one:

Problem 10:

You are given two lines $l_1$ and $l_2$ with some labeled angles.

• There is a 56° angle on line $l_2$, and an expression for another angle: $12 - 2(5x + 4)$.

Solution Strategy:

• Based on the angle relationships, it looks like the angles are corresponding angles or vertically opposite angles, meaning we can set them equal to each other to solve for $x$.

Set the given expression equal to 56°: $12 - 2(5x + 4) = 56$ Solve this equation step by step: $12 - 2(5x + 4) = 56$ $12 - 10x - 8 = 56$ $4 - 10x = 56$ $-10x = 56 - 4$ $-10x = 52$ $x = \frac{52}{-10} = -5.2$

Thus, $x = -5.2$.

Problem 11:

This problem involves several angles around the intersection of lines $l_1$ and $l_2$.

• One of the angles is labeled 49°, and another is labeled 45°.

Solution Strategy:

• Since these lines seem to have a transversal, you can check for alternate interior angles or corresponding angles to determine if the lines are parallel.
• Add the angles that form a straight line to check if the sum equals 180°, which might help conclude if the lines are parallel.

For $l_1$ and $l_2$, there may not be enough information without specific instructions, so the conclusion might be "Cannot be determined."

Extension Question (Solving for $x$ and $y$):

You are asked to solve for $x$ and $y$ in a geometric diagram of a quadrilateral.

• One of the angles is 140°, and two angles are expressed in terms of $x$ and $y$ (specifically, $3x$ and $y$).

Solution Strategy:

• The sum of the interior angles of a quadrilateral is always 360°. So you can write the equation: $140 + 3x + y + (\text{other angle}) = 360$ However, without knowing the fourth angle, it might be difficult to proceed further unless that missing information is provided.

Would you like to clarify the missing angle or ask more details about one of the problems?

Here are five follow-up questions related to the concepts from these problems:

1. What are corresponding angles, and how do they help in determining if two lines are parallel?
2. How can vertically opposite angles be useful in geometry problems?
3. Can you explain how to calculate the interior angles of a quadrilateral?
4. Why do angles on a straight line always sum to 180°?
5. In what other situations might you use angle relationships to prove lines are parallel?

Tip: When working with angles and lines, always consider the relationships like corresponding angles, alternate interior angles, and supplementary angles—they are key in determining parallelism.