A carpenter wishes to ensure that two wooden rails
MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
A carpenter wishes to ensure that two wooden rails, a and b, remain parallel while constructing a ladder. He places a straight plank c across the rails so that it meets rail a at M and rail b at N. He measures the interior angles on the same side of the plank and finds them to be 64∘ and 116∘ respectively.
(i) Verify, with appropriate calculation, whether the pair of interior angles measured is supplementary.
(ii) Based on your verification, state whether the rails a and b are parallel. Give a clear reason.
(iii) If another plank d is placed so that it meets rails a and b on the opposite side of plank c, what should be the sum of the interior angles formed on the same side of plank d in order to keep the rails parallel? Explain briefly.