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

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In a sports equipment storage unit in Melbourne, two parallel metal shelves are connected by a diagonal support rod that acts as a transversal. The angle formed between the support rod and the upper shelf on the left side measures 61 degrees.

What is the exact measure, in degrees, of the co-interior angle between the support rod and the lower shelf 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. Two parallel metal shelves are connected by a diagonal support rod, which acts as a transversal crossing the parallel lines.
  2. The angle between the support rod and the upper shelf on the left side is given as 61 degrees.
  3. The co-interior angles formed between a transversal and two parallel lines are supplementary, meaning they add up to 180 degrees.
  4. Let the co-interior angle on the lower shelf on the same side (left side) be x degrees.
  5. Set up the equation: 61 + x = 180.
  6. Subtract 61 from both sides: x = 180 - 61.
  7. Perform the subtraction: 180 - 61 = 119.
  8. Therefore, the co-interior angle between the support rod and the lower shelf on the same side is 119 degrees.
  9. Verify: 61 + 119 = 180, confirming the supplementary property.
  10. The geometric rule for co-interior angles between parallel lines and a transversal is correctly applied.
  11. The solution satisfies the given conditions and uses only angle properties for parallel lines.
  12. The exact measure of the co-interior angle is 119 degrees.

Reference answer: 119

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