Math Problem Statement
Solution
We are tasked with solving for in the context of a rectangle with diagonal , and angles given as and .
Explanation:
- In a rectangle, the diagonals bisect each other and form two congruent triangles.
- Specifically, the angles and are complementary because the sum of angles in a triangle is , and in the rectangle.
Thus, the equation is:
Solve for :
Substitute the given expressions:
Combine like terms:
Subtract 2 from both sides:
Divide by 11:
Final Answer:
Would you like further details or clarifications?
Here are five related questions to expand your understanding:
- What is the measure of and when ?
- How does the property of diagonals in a rectangle contribute to this solution?
- What other types of polygons have complementary angles in specific cases?
- How can you verify the solution geometrically?
- Can you apply this approach to parallelograms with different properties?
Tip: Always confirm angle relationships (like complementary or supplementary) in geometric problems to set up accurate equations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Properties of Rectangles
Complementary Angles
Formulas
m∠RTU + m∠STR = 90°
Theorems
The diagonals of a rectangle form congruent triangles
The sum of angles in a triangle is 180°
Suitable Grade Level
Grades 8-10
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