In this video lesson, students see that angles do not need to be adjacent to be complementary or supplementary. Students are also introduced to and begin to use the term vertical angles for describing the opposite angles formed when two lines cross. They examine multiple examples and see that the vertical angles have equal measures. Students can relate this understanding to the fact that both angles in a pair of vertical angles are supplementary to the same angle in between. By the end of the lesson, students will be able to see the different ways of making pairs of supplementary angles in two crossing lines.
In this video lesson, students are introduced to the terms complementary, for describing two angles whose measures add to 90°, and supplementary, for describing two angles whose measures add to 180°. They practice finding an unknown angle given the measure of another angle that is complementary or supplementary. Students realize that many angles share the same vertex as other angles, so they must be precise when naming each angle (MP6) in addition to describing the relationship between pairs of angles.
Grade 7, Episode 22: Unit 7, Lesson 2 | Illustrative Math
You'll learn how to prove that every trapezoid has two pairs of supplementary angles with this interactive video from the School Yourself Geometry series.
In Module 3, Topic B, students use linear equations and inequalities to solve problems. They continue to use bar diagrams from earlier grades where they see fit but will quickly discover that some problems would more reasonably be solved algebraically (as in the case of large numbers). Guiding students to arrive at this realization on their own develops the need for algebra. This algebraic approach builds upon work in Grade 6 with equations (6.EE.B.6, 6.EE.B.7) to now include multi-step equations and inequalities containing rational numbers (7.EE.B.3, 7.EE.B.4). Students solve problems involving consecutive numbers, total cost, age comparisons, distance/rate/time, area and perimeter, and missing angle measures. Solving equations with a variable is all about numbers, and students are challenged with the goal of finding the number that makes the equation true. When given in context, students recognize that a value exists, and it is simply their job to discover what that value is. Even the angles in each diagram have a precise value, which can be checked with a protractor to ensure students that the value they find does indeed create a true number sentence.
In Module 6, Topic A, students solve for unknown angles. The supporting work for unknown angles began in Grade 4, Module 4 (4.MD.C.5–7), where all of the key terms in this Topic were first defined, including adjacent, vertical, complementary, and supplementary angles, angles on a line and angles at a point. In Grade 4, students used those definitions as a basis to solve for unknown angles by using a combination of reasoning (through simple number sentences and equations), and measurement (using a protractor). For example, students learned to solve for a missing angle in a pair of supplementary angles where one angle measurement is known.
In Grade 7, Module 3, students studied how expressions and equations are efficient ways to solve problems. Two lessons were dedicated to applying the properties of equality to isolate the variable in the context of missing angle problems. The diagrams in those lessons were drawn to scale to help students more easily make the connection between the variable and what it actually represents. Now in Module 6, the most challenging examples of unknown angle problems (both diagram-based and verbal) require students to use a synthesis of angle relationships and algebra. The problems are multi-step, requiring students to identify several layers of angle relationships and to fit them with an appropriate equation to solve. In this case, they use angle relationships to find the measurement of an angle.
