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# 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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