Math Problem Statement
Solution
We are given a geometry problem where:
- AB is parallel to EC,
- ∠BCD = 72°,
- We are tasked to find ∠BAC.
Step-by-step Solution:
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Using the property of parallel lines: Since AB is parallel to EC, the angles ∠BAC and ∠BCD are alternate interior angles. Thus, we have:
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Given angle: It is provided that ∠BCD = 72°.
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Conclusion: Hence, ∠BAC = 72°.
Thus, the value of ∠BAC is 72°, and the correct option is (4).
Would you like any further details or explanations?
Relative Questions:
- What is the relationship between alternate interior angles in parallel lines?
- How do we use the properties of parallel lines to find unknown angles?
- What is the sum of the interior angles of a triangle, and how can it help in angle calculations?
- How can we use angle properties in circles (such as cyclic quadrilaterals)?
- What other problems can be solved using the properties of parallel lines and angles?
Tip:
When working with angles involving parallel lines, always look for corresponding or alternate angles as they often hold key information for solving the problem.
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Math Problem Analysis
Mathematical Concepts
Geometry
Parallel Lines
Angles in Circles
Formulas
Alternate Interior Angles Property
Theorems
Parallel Lines Theorem
Cyclic Quadrilateral Theorem
Suitable Grade Level
Grades 9-11
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