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

  • ABCDEFGABC \parallel DEFG
  • AEHAEH and BFHBFH are straight lines (transversals).
  • From the diagram:
    • 53\angle 53^\circ and xx are angles we need to relate.

Step 2: Use Angle Relationships

  1. Corresponding Angles:

    • If two lines are parallel and a transversal intersects them, the angles in corresponding positions are equal.
    • 53\angle 53^\circ (at BB) corresponds to E\angle E (below xx).
  2. Straight Line Property:

    • Angles on a straight line add up to 180180^\circ.
    • Along AEHAEH, x+E=180x + \angle E = 180^\circ.

Step 3: Calculate xx

  • From corresponding angles, E=53\angle E = \angle 53^\circ.
  • Substituting into the straight-line property: x+53=180x + 53^\circ = 180^\circ Simplify: x=18053=127x = 180^\circ - 53^\circ = 127^\circ

Final Answer:

The size of xx is 127127^\circ.


Would you like a detailed diagram or further explanations for any part of the solution?


5 Related Questions:

  1. What are corresponding angles, and why are they equal when lines are parallel?
  2. How does the property of angles on a straight line apply in other geometric problems?
  3. What are alternate interior angles, and how are they used in similar problems?
  4. How can we prove that two lines are parallel using angle properties?
  5. Can xx 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