NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Angles on parallel lines

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Required skills (click to reveal)

In a community garden in Sydney, two parallel garden beds are separated by a diagonal path that acts as a transversal. At one intersection, the angle between the path and the edge of the upper garden bed measures 57 degrees.

At the corresponding intersection on the lower garden bed, the angle formed between the path and the edge is labeled as x. What is the exact measure, in degrees, of angle x?

Answer as a single exact value.

Concept illustrations

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Adjacent angles on a straight line. The straight angle is 180°. The ray splits it into 65° and 115°, so the two adjacent angles sum to 180°. Drawing is schematic.65°115°65° + 115° = 180°
The straight angle is 180°. The ray splits it into 65° and 115°, so the two adjacent angles sum to 180°. Drawing is schematic.
Triangulating a pentagon. Two diagonals from one vertex split this pentagon into three triangles. Its interior-angle sum is 3 × 180° = 540°.(5 − 2) × 180° = 540°
Two diagonals from one vertex split this pentagon into three triangles. Its interior-angle sum is 3 × 180° = 540°.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. Two parallel garden beds are separated by a diagonal path that acts as a transversal. This forms angles at the intersections between the path and the edges of the garden beds.
  2. The angle between the path and the edge of the upper garden bed is given as 57 degrees.
  3. Since the garden beds are parallel and the path is a transversal, the corresponding angles formed at the intersections are equal.
  4. Angle x is the corresponding angle to the 57-degree angle on the lower garden bed.
  5. By the property of corresponding angles when two parallel lines are cut by a transversal, corresponding angles are congruent.
  6. Therefore, angle x must be equal to 57 degrees.
  7. No conversion or calculation is needed because the angle measure is already in degrees and the relationship is direct.
  8. The value of x is exactly 57 degrees.
  9. Verification: In a pair of parallel lines cut by a transversal, corresponding angles are equal. The given angle and x are corresponding angles, so they must be equal.
  10. The solution is consistent with geometric principles and the given data.
  11. The measure of angle x is 57 degrees.
  12. Final answer confirmed: angle x is exactly 57 degrees.

Reference answer: 57

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