Math Problem Statement
Solution
The problem involves determining the measures of angles and , given that is a straight angle (180°). Additionally, you are provided with expressions for the angles:
The total measure of the straight angle is:
Step 1: Set up the equation
Substitute the given expressions for and :
Step 2: Simplify the equation
Combine like terms:
Step 3: Solve for
Subtract 5 from both sides:
Divide by 25:
Step 4: Find the measures of the angles
Substitute back into the expressions for and :
Step 5: Verify the result
Check that the sum equals 180°:
The solution is correct.
Final Answer:
Would you like further clarification or additional help?
Here are 5 related questions to deepen your understanding:
- What is the definition of a straight angle, and how is it applied in such problems?
- How would you set up equations for other types of angles (e.g., complementary or supplementary)?
- If were given instead, how would you solve for ?
- What happens if you receive no algebraic expressions, just numerical values for these angles?
- Can this problem be extended to a triangle? If so, how?
Tip: Always double-check your solution by adding up all angle measures to verify the problem's conditions are met!
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Math Problem Analysis
Mathematical Concepts
Algebra
Angles in Geometry
Straight Angles
Formulas
Sum of angles in a straight angle: m∠RQS + m∠TQS = 180°
Expression substitution and solving equations
Theorems
Straight Angle Theorem
Suitable Grade Level
Grades 7-10