A carpenter installs two wooden slats and intended to be parallel in a window frame
MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
A carpenter installs two wooden slats S1 and S2 intended to be parallel in a window frame. To check accuracy, he places a straight measuring stick M that intersects both slats. Because of a small warp in the stick, the angle between M and S1 on the upper side is measured as 92∘, while the angle between M and S2 on the lower side is measured as 88∘. Manufacturing guidelines require that the slats be parallel within a tolerance of 3∘ on any angle measurement. Answer the questions below.
(i) Identify the special pair of angles referenced in the measurements.
(ii) Calculate the difference between the two measured angles.
(iii) Determine, with justification, whether the slats meet the manufacturing guideline for parallelism.
(iv) If the carpenter adjusts only the lower end of S2, by how many degrees must the angle at that point be changed to make the slats exactly parallel?