Construct with ruler and compasses, angles of following measures:
(a) 60°
(b) 30°
(c) 90°
(d) 120°
(e) 45°
(f) 135°
Solution:
We will be using the concept of angles to solve this.
(a) Angle of 60°
Step I: On a plane, sheet draw a line segment AB
Step II: Take B as a center, draw an arc with proper radius.
Step III: Take D as a center and with the radius of the same length mark an arc on the former arc at a point E.
Step IV: Join points B to E and produce up to point C. Thus the required angle is ∠ABC of measure 60°.
(b) Angle of 30°
Steps of construction:
Step I: On a plane, sheet draw a line segment AB
Step II: Take B as a center, draw an arc with proper radius.
Step III: Take D as the center and with the radius of the same length mark an arc on the former arc at a point E.
Step IV: Join points B to E and produce up to point C. Thus the required angle is ∠ABC of measure 60°.
Step V: Now, draw line segment BF as the bisector of ∠ABC.
Thus ∠ABF = 60/2 = 30°.
(c) Angle of 90°
Steps of construction:
Step I: Draw a line segment AB on a plane sheet.
Step II: With the center, B draw an arc that meets AB at C.
Step III: Take C as a center and with the same radius, mark two small arcs D and E on the former arc.
Step IV: Take D and E as centers and with the same radius, draw two arcs that meet each other at point C.
Step V: Join points B and C such that ∠ABC = 90°
(d) Angle of 120°.
Step I: Draw a line segment AB.
Step II: With A as a center and draw an arc of proper length.
Step III: Take D as a center with the same radius, draw two marks E and F on the former arc.
Step IV: Join points A to F and produce to point C. Thus ∠CAB = 120°
(e) Angle of 45°, i.e., 90°/2= 45°
Steps of construction:
Step I: Draw a line segment AB on a plane sheet.
Step II: With the center, B draw an arc that meets AB at C.
Step III: Take C as a center and with the same radius, mark two small arcs D and E on the former arc.
Step IV: Take D and E as centers and with the same radius, draw two arcs that meet each other at point G.
Step V: Join points B and G such that ∠ABG = 90°
Step VI: Draw the angle bisector BH of ∠ABG such that ∠ABH = 45°.
(f) An angle of 135°
Since 135° is a sum of angle 90° and angle 45°.
= 90° + (90/2 )°
Step1: Draw a line segment l and mark a point P on the line. Take P as the center, draw a semicircle that intersects the line l at Q and R, respectively.
Step2: Take R as a center and with the same radius, draw an arc that intersects the previously drawn arc at S
Step3: Now, take S as the center, and with the same radius, draw an arc such that it intersects the arc at T.
Step4: Draw arcs of the same radius from point S and T as centers that intersect each other at point U.
Step5: Join point PU which intersects the arc at V. Now take points Q and V as centers and with the radius draw arcs(radius more than 1/2) that intersect each other at point W.
Step6: Join the points PW with a line segment.
Thus, ∠WPR is 90° with line l.
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 Question 5
Construct with ruler and compasses, angles of following measures: (a) 60° (b) 30° (c) 90° (d) 120° (e) 45° (f) 135°
Summary:
With the help of a ruler and compasses, the given angles were constructed.
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