Students are taught definitions of complementary (sum 90°), supplementary (sum 180°), vertical (opposite angles congruent), and adjacent angles, and they complete practice problems using those facts. The materials show worked numerical examples that solve for unknown angles (e.g., 90° - 40° = 50° and 180° - 110° = 70°) and include activity questions asking students to find missing angle measures given complementary, supplementary, or vertical relationships. The answer key includes specific problems where students compute unknown measures (e.g., given 65° and a supplementary relationship, find 115°).

Students identify and use vertical and complementary relationships in the first example where they find n by noting the 32° vertical angle and then computing the complementary angle 90 - 32 = 58. Students write equations from diagrams in Activity 2 (examples: 126 + n = 180, n + 2n = 90, and 5n = n + 92) to represent supplementary, complementary, and vertical angle relationships. Activity 3 has students solve those equations algebraically (e.g., subtract n then divide in 5n = n + 92) and substitute the solution back into expressions to find actual angle measures. Multiple student activity pages require forming and solving multi-step equations (for example n + 2n + n + 48 = 180 and 2n + 3n = 180) that combine angle relationships and algebraic steps.

Students are asked to write and solve equations for angle measures (Unit 6 Quiz question 9 shows the equation 104 + n = 180 and the solution n = 76°). Quiz items and activities explicitly use supplementary, complementary, and vertical angle relationships to find unknowns (Quiz #8 a–c finds angles using vertical, complementary, and supplementary facts). Activity 5 has students identify corresponding/ congruent angles and then use angle-sum reasoning to compute missing angles (e.g., using a 40° corresponding angle and an 80° angle to find a third angle of 60°).

Students solve explicit problems involving complementary, supplementary, vertical, and adjacent angles (e.g., Section I problems asking for n when angles are complementary or supplementary; a vertical-angle problem with a 60° given). Students write and solve algebraic equations from angle relationships (e.g., question 5: n + 2n + (3n + 12) = 180 and question 6: 3n = 2n + 35) and the answer key shows the algebraic steps to find n. The Parent Plan and activity pages explicitly instruct students to use angle-relationship facts to write and solve equations for unknown angle measures.

The Parent Plan Skills explicitly states that students should "Use facts about supplementary, complementary, vertical, and adjacent angles to solve for an unknown angle." The Student Activity "Solve the Missing Angle Problem" instructs students to create a problem involving supplementary, complementary, and/or vertical angles, construct a diagram, and provide a solution key. The unit's "Ideas to Think About" asks "What could a variable represent in a geometry problem?" and the sample planning card for a reflex angle shows students computing an unknown angle by arithmetic (subtracting from 360°).

Students are asked to find the complement and supplement of a 36° angle (Problem 1), which practices complementary and supplementary angle facts. In Problem 2 students are given intersecting lines with angle measures 3n and 2n + 16, are instructed to write and solve an equation (3n = 2n + 16), and then use the solution to find the angle measures, which practices writing and solving equations from vertical angle relationships. The answer key shows the algebraic solution and substitution to find the actual angle measures.

Students identify and label vertical, adjacent, supplementary, complementary, and congruent angles in Activity 1 and the Transversals notes. Students use the Triangle Sum Rule and the Exterior Angle Rule to compute missing triangle angles in Activity 2 and Activity 3. In Activity 5 and related worksheets, students fill in all missing angles on diagrams of parallel lines and transversals, applying multiple angle relationships across a single diagram.

Students solve triangle-angle problems (e.g., Problems 21 and 22) where they compute a missing interior angle and an exterior angle using angle-sum and exterior-angle reasoning. Students complete Problem 23, finding measures of multiple angles formed by intersecting lines and identifying rules such as VA (vertical) and S (supplementary). The answer key and problems explicitly identify complementary and vertical relationships (e.g., Problem 17 and its key indicating complementary angles and a statement that vertical angles are congruent).

Students are instructed to draw two parallel lines with a transversal and to color and identify angle types in the "Colorful Angle Relationships" activity (vertical, alternate interior, alternate exterior, corresponding). The Student Activity asks students to pick a recognizable color for each angle type, which requires them to locate and distinguish angle pairs created by a transversal. Parent notes also list angle relationships and mention supplementary angles in the checklist of required geometric components.

Activity 3 explicitly asks students to identify and use vertical angles (Problem 1), linear pairs/supplementary angles (Problem 2), triangle angle sum and exterior angle relationships (Problems 3 and 4), and corresponding/supplementary angles with parallel lines (Problems 5–7). Problem 8 asks students to write an equation for complementary angles where one angle is twice the other and solve it; the answer key shows the equation 2x + x = 90 and solves for the measures. The answer key and tasks require students to set up numerical relationships among angle measures and solve for unknowns.

Students are asked in problem 20 to find two complementary angles where one angle is twice the other, which requires writing an equation (A = 2B, A + B = 90) and solving for both measures. Problem 21 asks students to find all related angles when two lines are cut by a transversal given one angle measure, which requires using vertical, corresponding/alternate, and supplementary relationships to determine multiple angle measures. The answer key explicitly shows solutions using complementary (Angle A and B = 60° and 30°) and uses 180°−65° to find adjacent (supplementary) angles and identifies vertical/corresponding/alternate interior angles as 65°.