Math Problem Statement
In the figure, m∠1 = (x−12)° and m∠2 = (5x)°. (a) Write an equation to find x. (b) Find the degree measure of each angle.
Solution
To solve the problem, let's break it down step by step:
Given:
Observations:
- and are adjacent angles forming a straight line.
- The sum of the angles on a straight line is .
(a) Write an equation to find :
The equation can be written as:
Substitute the given expressions for and :
Simplify the equation:
Add 12 to both sides:
Divide both sides by 6:
(b) Find the degree measure of each angle:
Now that , substitute into the expressions for and .
-
:
-
:
Final Answers:
- Equation:
- Degree Measures:
Let me know if you need any clarifications!
Related Questions:
- What is the sum of adjacent angles on a straight line?
- How would you solve for if and were vertical angles?
- What is the general formula for angles that form a linear pair?
- If instead, how would the solution change?
- How can you check if your solutions for and are correct?
Tip:
Always check your final answers by verifying that the sum of the angles equals .
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Math Problem Analysis
Mathematical Concepts
Linear Pairs
Angle Relationships
Basic Algebra
Formulas
Sum of angles on a straight line = 180°
Theorems
Linear Pair Theorem
Suitable Grade Level
Grades 6-8