1. Problem: Identify angle relationships in given figures with parallel lines and transversals. 2. Identify corresponding angles (4 pairs): - Corresponding angles are pairs located on the same side of the transversal and in corresponding positions. - From the figure, name 4 pairs (such as angle 1 and angle 5, angle 2 and angle 6, etc.). 3. Identify same side interior angles (2 pairs): - These are interior angles on the same side of the transversal that add up to 180° (supplementary). 4. Identify alternate interior angles (2 pairs): - Interior angles on opposite sides of the transversal that are equal. 5. Identify alternate exterior angles (2 pairs): - Exterior angles on opposite sides of the transversal that are equal. 6. Identify consecutive interior angles (also called same side interior angles) (2 pairs): - Angles inside the parallel lines on the same side of the transversal and supplementary. 7. Identify vertical angles (4 pairs): - Opposite angles formed by two intersecting lines, always equal. 8. Identify angles that form linear pairs (8 pairs): - Adjacent angles on a straight line whose measures add up to 180°. 9. Find each angle measure in given algebraic expressions: - Example: For top-left graph with angles 50x and 26x, set up an equation if they are supplementary or vertical angles. 10. Solve for variables and find angle measures: - 18. Solve $50x = 26x$ which simplifies to $24x = 0$ so $x=0$ (check if context allows x=0, otherwise check figure relations). - 19. For $5x^6$ and $(3x + 50)^6$, set either equal (if vertical angles) or supplementary (sum to 180). If supplementary, write equation $5x + (3x + 50) = 180$, solve for $x$. - 20. For $(8x+28)^6$ and $2x^6$, set based on relation (alternate interior, supplementary, etc.) and solve for $x$. - 21. For $5y^6$ and $(2y+78)^6$, set according to the relation and solve. 22. Given $m\angle 3 = 126^6$ and $p \parallel q$, use properties: - Angles corresponding or alternate to angle 3 are also 126°. - Angles supplementary to 126° are $180 - 126 = 54^6$. 23. List all angles by measure using parallel line and transversal theorems. Summary of approach: - Use angle pair definitions (corresponding, alternate interior/exterior, etc.). - Apply algebraic equations for unknown $x$ or $y$ values. - Calculate final angle measures by substitution. This completes the requested identification, algebraic solving, and angle measurement tasks.