Adjacent Angles and Solving Equations
Adjacent angles and solving equations is a Grade 7 geometry skill in Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings. Adjacent angles share a common vertex and side but do not overlap, and their measures add up to the total angle they create together. When adjacent angles form a right angle (90 degrees) or straight angle (180 degrees), you can set up and solve an equation to find unknown angle values.
Key Concepts
Property Adjacent Angles are two angles that are side by side. They must meet two rules: 1. They share a common vertex (corner). 2. They share a common side (ray) between them, with no overlapping insides. Key Rule: The measures of two adjacent angles add up to the measure of the larger total angle they create.
Examples Basic: $\angle AOB$ and $\angle BOC$ share vertex O and side OB. If $\angle AOB$ is 30° and $\angle BOC$ is 45°, the total large angle $\angle AOC$ is 30 + 45 = 75°. Forming a Right Angle: Two adjacent angles form a 90° corner. One is $(3x + 10)$° and the other is $(2x 5)$°. Equation: $$(3x + 10) + (2x 5) = 90$$ $$5x + 5 = 90$$, so $5x = 85$, meaning $x = 17$. Forming a Straight Angle: Two adjacent angles make a flat 180° line. If one is 65°, the other must be 180 65 = 115°.
Explanation Think of adjacent angles like two adjoining rooms in a house that share a single wall. They don't overlap, but together they make up the total space! When you know what kind of larger angle they form together (like a 90° corner or a 180° flat line), you can simply add their two expressions together and set them equal to that total number to solve the math puzzle.
Common Questions
What are adjacent angles?
Adjacent angles share a common vertex and exactly one common side, with no overlapping interiors. Together they form a larger angle equal to the sum of both individual angles.
How do you use adjacent angles to write equations?
Identify the total angle the adjacent angles form (like 90 degrees or 180 degrees), set the sum of the two angle expressions equal to that total, and solve the equation.
What is an example of solving an equation with adjacent angles?
If two adjacent angles form a right angle, and they measure (3x plus 10) and (2x minus 5), then set (3x plus 10) plus (2x minus 5) equals 90, solve to get 5x plus 5 equals 90, so x equals 17.
What textbook covers adjacent angles and solving equations in Grade 7?
Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings covers adjacent angle properties and using them to solve algebraic equations.