A city planner marks two straight guide lines and on the ground to indicate where…
MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles
Problem
A city planner marks two straight guide lines g1 and g2 on the ground to indicate where future bicycle lanes will run. A surveyor’s measuring pole p crosses both guide lines. At the intersection with g1, the angle between the pole and the guide line on the north-east side is measured as 68∘. At the intersection with g2, the angle between the pole and the guide line on the south-west side is also found to be 68∘. Answer the following questions.
(i) Identify the special pair of angles that are equal in this situation.
(ii) Explain, with reason, whether the two guide lines g1 and g2 must be parallel.
(iii) Name the theorem that justifies your answer in part (ii).