Math Problem Statement
ABC and DEFG are parallel. AEH and BFH are straight lines. Work out the size of angle marked x°. Give reasons for each property that you used.
Solution
The given problem involves working with parallel lines, angles, and reasoning using geometric properties. Let’s solve this step-by-step:
Step 1: Identify the Parallel Lines and Properties
- and are straight lines (transversals).
- From the diagram:
- and are angles we need to relate.
Step 2: Use Angle Relationships
-
Corresponding Angles:
- If two lines are parallel and a transversal intersects them, the angles in corresponding positions are equal.
- (at ) corresponds to (below ).
-
Straight Line Property:
- Angles on a straight line add up to .
- Along , .
Step 3: Calculate
- From corresponding angles, .
- Substituting into the straight-line property: Simplify:
Final Answer:
The size of is .
Would you like a detailed diagram or further explanations for any part of the solution?
5 Related Questions:
- What are corresponding angles, and why are they equal when lines are parallel?
- How does the property of angles on a straight line apply in other geometric problems?
- What are alternate interior angles, and how are they used in similar problems?
- How can we prove that two lines are parallel using angle properties?
- Can be calculated differently in this problem? If so, how?
Tip:
Always look for relationships like corresponding, alternate interior, or co-interior angles when working with parallel lines and transversals!
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles in Parallel Lines
Transversals
Linear Pair of Angles
Formulas
Angles on a straight line add up to 180°
Theorems
Corresponding Angles Theorem
Supplementary Angles Theorem
Suitable Grade Level
Grades 8-10