Puzzle: Angle Geometry: Name | PDF - Free Printable

1. Identify the given angles and relationships in the diagram.
2. Use the properties of parallel lines and transversals to find unknown angles.
3. Apply the triangle angle sum property (sum of angles in a triangle is 180°).
4. Use the fact that angles on a straight line sum to 180°.
5. Use the property that corresponding angles are equal when two parallel lines are cut by a transversal.
6. Use the property that alternate interior angles are equal when two parallel lines are cut by a transversal.
7. Use the property that vertical angles are equal.
8. Calculate each unknown angle step by step using the above properties.

For the first diagram:
- The angle at the top of the triangle is 85°, and one base angle is 48°.
- The third angle in the triangle can be found as 180° - 85° - 48° = 47°.
- The angle marked as 143° is an exterior angle to the triangle, so the adjacent interior angle is 180° - 143° = 37°.
- Use the properties of parallel lines and the transversal to find other angles.

For the second diagram:
- The angle 110° and 115° are on a straight line with other angles, so their adjacent angles can be found.
- Use the fact that the sum of angles around a point is 360°.
- Use the properties of parallel lines to find corresponding and alternate angles.
- Calculate each unknown angle using the relationships.

Final answers for the unknown angles:
- In the first diagram: 47°, 37°, and other angles derived from parallel lines and transversals.
- In the second diagram: angles derived from given angles and properties of parallel lines and transversals.

Note: The exact values depend on the specific configuration and relationships in the diagram, which are not fully described in text. The solution involves applying geometric principles step by step.