Math Problem Statement
Given that
BA
and
BD
are opposite rays, m∠CBA=12n+4, and m∠DBC=14n−6, find m∠ABC.
Solution
Given that and are opposite rays, this means that the angles and are adjacent angles on a straight line. The sum of the measures of these angles must therefore be 180°, because they form a linear pair.
Given:
Since and form a straight line, we can set up the following equation:
Now, let's solve for :
- Combine like terms:
- Add 2 to both sides:
- Divide both sides by 26:
Now that we know , we can substitute it back into the expressions for and :
Thus, the measure of , which is the entire straight line, is:
This confirms that the angles form a linear pair, and is .
Would you like more details or have any questions? Here are 5 related questions to expand on this topic:
- What are opposite rays, and how do they relate to straight angles?
- How do linear pairs of angles help in solving angle problems?
- What is the difference between adjacent and supplementary angles?
- How would the problem change if the angles were complementary instead of forming a straight line?
- Can you explain the relationship between linear pairs and vertical angles?
Tip: Always remember that opposite rays create a straight angle, meaning the sum of the angles must equal 180°.
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Math Problem Analysis
Mathematical Concepts
Angles
Linear pairs
Opposite rays
Formulas
-
Theorems
-
Suitable Grade Level
Grades 9-10