# NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 (Ex. 14.6) Practical Geometry in English Medium and Hindi Medium updated for CBSE Session 2021-2022. All the contents are designed and prepared as per the latest CBSE Syllabus 2021-22.

In Class 6 math exercise 14.6 deals with the questions related to angle formation and their bisectors. Step by step solutions are given in PDF and videos solutions with complete explanation.## Class 6 Maths Chapter 14 Exercise 14.6 Solution

### CBSE NCERT Class 6 Maths Chapter 14 Exercise 14.6 Solution in Hindi and English Medium

Class: 6 | Mathematics |

Chapter: 14 | Practical Geometry |

Exercise: 14.6 | Hindi and English Medium Solutions |

### Class 6 Maths Chapter 14 Exercise 14.6 Solution in Videos

##### Construction of Angles of Special Measures

There are some elegant and accurate methods to construct some angles of special sizes without the use

##### I. To Construct an Angle of 60°

We take the following steps for this construction:

Step-1: Draw a ray BC.

Step-2: With B as centre and any suitable radius draw an arc above BC cutting BC at R.

Step-3: With R as centre and same radius cut the arc at S.

Step-4: Join BS and produce it to A.

Step-5: Then angle ABC is the required angle of 60°.

##### II. To construct an Angle of 30°

Observe that 30° = ½ × 60°.

We therefore, follow the procedure of bisecting a given angle learnt in previous section to get the required angle. Thus, to construct an angle of 30°, we proceed as follows:

Step-1: Draw an angle ABC = 60° as done above.

Step-2: Bisect angle ABC.

Step-3: Then angle RBC = 30° and also angle ABR = 30°.

##### III. To Construct an Angle of 90°

We take the following steps for this construction:

(i) Draw a ray BC.

(ii) With B as centre and any suitable radius draw an arc cutting BC at D.

(iii) With D as centre and same radius cut the arc at E and then with E as centre and the same radius cut the arc again at F.

(iv) With E and F as centres and any suitable radius draw arcs cutting each other at P.

(v) Join BP and produce to A. Then angle ABC is the required angle, i.e., 90°.

##### IV. To Construct an Angle of 45°

We take the following steps for this construction:

(i)Draw an angle ABC = 90°.

(ii) With D as centre and radius more than half of DE draw an arc.

(iii) With G as centre and same radius as above, draw another arc cutting the first arc at H.

(iv) Join BH and produce to M.

Then angle CBM is the required angle of 45° and also angle MBA is 45°.

##### V. To Construct an Angle of 120°

We take the following steps for this construction:

Step-1: Draw a ray BC.

Step-2: With B as centre and any suitable radius draw an arc cutting BC at D.

Step-3: With D as centre and same radius cut off the arc first at E and then with E as centre cut off the arc at another point F.

Step-4: Join BF and produce it to A. then angle ABC is the required angle of 120°.

### Class 6 Maths Exercise 14.6 Important Questions

##### What are the types of angles?

Different Types of Angles:

(i) Zero Angles.

(ii)Acute Angles.

(iii)Right Angles.

(iv)Obtuse Angles.

(v)Straight Angles.

(vi)Reflex Angles.

(vii)Complete Angle.

##### What are standard angles?

Trigonometric ratios are Sine, Cosine, Tangent, Cotangent, Secant and Cosecant. The standard angles for these trigonometric ratios are 0°, 30°, 45°, 60° and 90°. These angles are most commonly and frequently used in trigonometry.

##### How do you construct a 120 angle?

Constructing a 120° Angle: 120° angle can be constructed using the logic that 60° + 120° = 180°. Thus, we can understand that in order to construct 120° we can construct 60° angle and then further extend one of its arms.