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  1. Chapter 11 Class 9 Constructions
  2. Serial order wise
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Ex 11.1, 4 Construct the following angles and verify by measuring them by a Protractor : (i) 75 75 = 60 + 15 75 = 60 + (30 )/2 So, to we make 75 , we make 60 and then bisector of 30 Steps of construction Draw a ray OA. Taking O as centre and any radius, draw an arc cutting OA at B. Now, taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C. Now, with C as center, and same radius, draw another arc intersecting the previously drawn arc at point D. Thus, AOE = 60 and EOF = 60 Taking C and D as Centre , with radius more than 1/2CD, draw arcs intersecting at P. Join OP Thus, EOP = 30 Taking Q and C as Centre , with radius more than 1/2QC, draw arcs intersecting at R. Join OR Thus, AOR = 75 On measuring the AOR by protractor, we find that AOR = 75 Thus, the construction is verified (ii) 105 105 = 90 + 15 105 = 90 + (30 )/2 So, to make 105 , we make 90 and then bisector of 30 Steps of construction Draw a ray OA. Taking O as centre and any radius, draw an arc cutting OA at B. Now, taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C. With C as centre and the same radius, draw an arc cutting the arc at D. With C and D as centres and radius more than 1/2 CD draw two arcs intersecting at P. Join OP. Thus, AOP = 90 Join OD POD = 30 as OP is bisector of COD. With Q and D as centres and radius more than 1/2 DQ draw two arcs intersecting at R. Join OR Thus, POR = 15 AOR = AOP + POR = 90 + 15 AOR = 105 (iii) 135 135 = 90 + 45 So, to make 135 , we make 90 and then 45 Steps of construction Draw a line OAA . Taking O as centre and any radius, draw an arc cutting OA at B. Now, taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point C. With C as centre and the same radius, draw an arc cutting the arc at D. With C and D as centres and radius more than 1/2 CD draw two arcs intersecting at P. Join OP. Thus, AOP = 90 Also, A OP = 90 So, to we bisect A OP 7.With B and Q as centres and radius more than 1/2 B Q draw two arcs intersecting at R. 8.Join OR. A OR = 45 POR = 45 Thus, AOR = AOP + POR = 90 + 35 AOR = 135

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.