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

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In a craft design for a folding wooden picture frame in Melbourne, two parallel horizontal edges are connected by a diagonal support strut that acts as a transversal. The angle formed between the strut and the top edge on the left side measures 89 degrees.

What is the exact measure, in degrees, of the corresponding angle formed between the strut and the bottom edge on the same side of the transversal? 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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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The problem involves two parallel horizontal edges connected by a diagonal transversal strut in a wooden picture frame in Melbourne.
  2. The angle between the transversal strut and the top edge on the left side is given as 89 degrees.
  3. Since the two horizontal edges are parallel and the strut is a transversal, the corresponding angles formed on the same side of the transversal are equal.
  4. The corresponding angle is formed between the same transversal strut and the bottom edge on the same side (left side) of the transversal.
  5. By the property of corresponding angles when two parallel lines are cut by a transversal, corresponding angles are congruent.
  6. Therefore, the measure of the corresponding angle on the bottom edge is equal to the given angle on the top edge.
  7. Substitute the given value: 89 degrees.
  8. No conversion is needed because the angle is already in degrees and the property applies directly.
  9. The corresponding angle is exactly 89 degrees.
  10. This result is consistent with the geometric rule for corresponding angles.
  11. The exact measure of the corresponding angle is 89 degrees.
  12. The solution is complete and matches the geometric principle for parallel lines and transversals.

Reference answer: 89

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