You've uploaded images containing a worksheet on angles and parallel lines. Let's work through the problems step by step.

Image 1 Breakdown:

1. Problems 10 to 15 involve finding the measure of angles in various geometric shapes and applying angle relationships like:
   • Triangle Angle Sum Theorem (sum of angles in a triangle is always 180°).
   • Linear Pair (two adjacent angles on a straight line add up to 180°).
   • Exterior Angle Theorem (an exterior angle of a triangle is equal to the sum of the two opposite interior angles).

Image 2 Breakdown:

1. Parallel Lines and Triangle Angle Sums:
   • These involve equations for angles formed by parallel lines and a transversal, and using the properties of angles in a triangle to solve for unknowns. Common rules here include:
     • Corresponding Angles (angles in matching corners when two lines are crossed by a transversal are equal).
     • Alternate Interior Angles (angles inside the parallel lines, on opposite sides of the transversal, are equal).
     • Triangle Angle Sum (sum of angles in any triangle is 180°).

Let's solve a couple of problems as examples:

Problem 10 (Image 1):

• Given a triangle with one angle labeled as 73° and another angle as 49°, the third angle can be found using the Triangle Angle Sum Theorem. $180° - (73° + 49°) = 180° - 122° = 58°$ So, the third angle is 58°.

Problem 2 (Image 2):

• A triangle has two angles labeled as 62° and 83°. Again, using the Triangle Angle Sum Theorem: $180° - (62° + 83°) = 180° - 145° = 35°$ Therefore, the unknown angle is 35°.

Would you like more specific solutions for other problems? Let me know if you need details on particular questions, and feel free to ask about any of the rules! Here are some relevant questions:

1. How do you apply the Exterior Angle Theorem to solve for unknown angles?
2. What is the best approach to find the measure of angles involving algebraic expressions?
3. How do alternate interior angles help in solving problems involving parallel lines?
4. What are supplementary angles and how are they useful in solving geometry problems?
5. How do you set up equations for angles in a polygon?

Tip: Always start by identifying the known angles and applying basic angle sum properties to find the unknowns.