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

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In a mechanical design for a folding shelf in a storage unit in Melbourne, two parallel horizontal rails are connected by a diagonal support beam. The beam forms an angle of 127 degrees with the upper rail on the left side.

What is the exact measure, in degrees, of the co-interior angle between the beam and the lower rail on the same side of the beam? Answer as a single exact value.

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Explanation

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Worked solution

  1. Two parallel horizontal rails are connected by a diagonal support beam, forming angles with each rail. The beam makes an angle of 127 degrees with the upper rail on the left side.
  2. The beam acts as a transversal crossing the two parallel lines (the rails). The angle given (127°) is on the same side of the transversal as the lower rail.
  3. Co-interior angles are the angles on the same side of the transversal and between the two parallel lines. They are supplementary, meaning their sum is 180 degrees.
  4. Let x be the co-interior angle between the beam and the lower rail on the same side. Then, by the co-interior angle property: x + 127° = 180°.
  5. Solve for x: x = 180° - 127°.
  6. Perform subtraction: 180 - 127 = 53.
  7. Therefore, x = 53°.
  8. The co-interior angle between the beam and the lower rail on the same side is 53 degrees.
  9. Check: 127° + 53° = 180°, which confirms the co-interior angle property.
  10. The solution is consistent with the geometric rule for parallel lines and transversals.
  11. The exact measure of the co-interior angle is 53 degrees.
  12. Final answer confirmed.

Reference answer: 53

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