Question 6 - Figure it out - Page 123, 124, 125 - Chapter 5 Class 7 - Parallel and Intersecting Lines (Ganita Prakash)

Transcript

Question 6 What is the measure of angle ∠NOP in Fig. 5.35? [Hint: Draw lines parallel to LM and PQ through points N and O.] First, we do what the hint says We draw lines parallel to LM and PQ through points N and O And, we also mark angles which it has cut in the figure. So, we have Red angle + Green angle = 96° Yellow angle + Purple angle = ∠ a Taking LM and red line passing through N as parallel lines And MN as transversal, Red angle & 40° are alternate interior angles, so they must be equal ∴ Red angle = 40° Also, Red angle + Green angle = 96° 40° + Green angle = 96° Green angle = 96° – 40° Green angle = 56° Taking the two red lines as parallel lines, and NO as transversal, Green angle & yellow angle are alternate interior angles, so they must be equal Yellow angle = Green angle Yellow angle = 56° Taking PQ and red line passing through O as parallel lines And OP as transversal, Purple angle & 52° are alternate interior angles, so they must be equal ∴ Purple angle = 52° Now, Yellow angle + Purple angle = ∠ a 56° + 52° = ∠ a 108° = ∠ a ∠ a = 108°