MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles
Problem
Three lines l1,l2 and l3 pass through the same point O. It is given that l1⊥l2 and the acute angle between l2 and l3 is 35∘.
(i) Draw a neat labelled sketch showing the three lines and the given information.
(ii) Using angle relationships at a point, prove that the acute angle between l1 and l3 is 55∘.
(iii) If l3 is now rotated about O so that it makes an angle of y∘ with l1 towards the opposite side of the angle calculated in part (ii), find—giving full justification—the measure of the angle between l2 and the new position of l3.