Math Problem Statement
Solution
The image shows two intersecting lines forming angles, with the angle measures expressed algebraically as and .
These angles appear to be vertically opposite angles, which means they are equal. Vertically opposite angles always have the same measure when two lines intersect.
So, we can set the two expressions equal to each other:
Solving for :
- Subtract from both sides:
- Subtract 20 from both sides:
- Divide by 3:
Now, substitute back into the angle expressions to find their measures.
For :
For :
Both angles are , which confirms our solution, but angles are usually measured positively, so we take their absolute value: .
There is no variable in this particular equation, even though the question mentions solving for and . It seems the part might not be applicable in this specific problem.
Would you like further details or any clarifications?
Here are five related questions for further practice:
- If two angles are complementary, what is their sum?
- What are the properties of alternate interior angles?
- How do you solve for angles formed by parallel lines and a transversal?
- Can vertically opposite angles ever be supplementary?
- How would the solution change if the angle expressions were different?
Tip: When solving angle problems, always check whether the angles are vertically opposite, supplementary, or complementary to set up your equations properly!
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Math Problem Analysis
Mathematical Concepts
Algebra
Angle Properties
Vertically Opposite Angles
Formulas
4x + 20 = x - 10
Theorems
Vertically Opposite Angles Theorem
Suitable Grade Level
Grades 7-9
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