Math Problem Statement
solve
Solution
The image shows two intersecting lines with angles formed. The problem is asking to find the value of and the measure of angle (denoted as ).
Step-by-Step Solution:
We have the following given expressions for the angles:
- for one of the angles
- for the angle marked as
Since these two angles are vertical angles, they are congruent. Therefore, we can set their expressions equal to each other:
Solving for :
-
Move the terms involving to one side:
-
Simplify:
-
Solve for :
Thus, .
Finding the measure of :
Substitute into either angle expression (since both are equal, you can use either one).
Using the expression for :
Thus, .
Final Answers:
Would you like a more detailed explanation, or do you have any questions?
Here are 5 related questions to explore:
- What are vertical angles, and why are they always congruent?
- How do you know when angles are supplementary or congruent?
- What other properties can you infer from intersecting lines and their angles?
- Can you generalize the steps to solve for when two angles are given as algebraic expressions?
- How would the solution change if the lines were parallel and we were dealing with corresponding angles?
Tip: Always check for angle relationships, such as vertical angles or supplementary angles, to set up equations when dealing with intersecting lines.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Linear Equations
Formulas
3x + 5 = 5x - 39
Theorems
Vertical Angles Theorem
Suitable Grade Level
Grades 8-10