Math Problem Statement
Solution
In the image, we have an angle that is split into two angles, labeled and . These two angles are adjacent, and together they form the larger angle , which is a straight line. A straight line measures , so we can set up an equation to find .
The two angles together must sum to :
Let's solve for :
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Combine like terms:
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Add 20 to both sides:
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Divide both sides by 9:
So, .
Now, we can substitute this value of back into the expressions for the angles:
The two angles are approximately and , which indeed sum to .
Would you like more details or have any questions?
Here are 5 related questions:
- What are adjacent angles, and how are they related?
- How would you solve a similar problem if the angles formed a triangle instead of a straight line?
- Can you explain how the sum of angles around a point adds up to 360 degrees?
- What is the difference between supplementary and complementary angles?
- How would the problem change if the sum of the two angles were 90 degrees instead of 180 degrees?
Tip: Always check that the sum of the calculated angles matches the expected total (e.g., 180° for straight angles or 360° for angles around a point).
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Angle Properties
Formulas
Sum of angles on a straight line: 180°
Algebraic expressions for angle measures
Theorems
Supplementary Angles Theorem
Suitable Grade Level
Grades 8-10
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