Finding Missing Angle Measures with Equations
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 12: Constructions and Scale Drawings) learn to find missing angle measures using equations. For complementary angles they set up x + known angle = 90, and for supplementary angles x + known angle = 180, then solve for x.
Key Concepts
Property To find an unknown angle measure, set up an equation using the sum property: For complementary angles: x + known angle = 90° For supplementary angles: x + known angle = 180°.
Examples If two angles are complementary and one measures 35°, find the other: x + 35 = 90, so x = 55°. Two supplementary angles where one is (2x + 10)° and the other is 70°. Find x: (2x + 10) + 70 = 180, so 2x + 80 = 180, therefore x = 50. Two complementary angles expressed as (3x 5)° and (x + 15)°. Find both angles: (3x 5) + (x + 15) = 90, so 4x + 10 = 90, therefore x = 20. The angles are 55° and 35°.
Explanation When one angle measure is known, you can find the unknown angle by setting up a simple equation. Subtract the known angle from 90° for complementary angles or from 180° for supplementary angles. If the angles contain variables, set up the addition equation and solve it using basic algebra.
Common Questions
How do you find a missing angle measure using equations in 7th grade?
For complementary angles: x + known angle = 90. Solve for x. For supplementary angles: x + known angle = 180. Solve for x.
How do you find a missing complementary angle?
If one angle is 35 degrees and angles are complementary: x + 35 = 90, so x = 55 degrees.
How do you solve for x when angles contain variables?
Set up the sum equation (90 or 180), substitute the algebraic expressions, and solve. Example: (3x-5) + (x+15) = 90 gives 4x+10 = 90, then x = 20.
What chapter in Big Ideas Math Advanced 2 covers finding missing angles with equations?
Chapter 12: Constructions and Scale Drawings in Big Ideas Math Advanced 2 (Grade 7) covers finding missing angle measures with equations.
What do complementary and supplementary mean?
Complementary angles sum to 90 degrees. Supplementary angles sum to 180 degrees.