Angles Class-6 RS Aggarwal ICSE Maths Goyal Brother Prakashan Chapter-15. We provide step by step Solutions of Exercise / lesson-15 Angles for ICSE Class-6 RS Aggarwal Mathematics.
Our Solutions contain all type Questions with Exe-15 A , Exe-15 B to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Mathematics.
| Board | ICSE |
| Publications | Goyal brothers Prakshan |
| Subject | Maths |
| Class | 6th |
| Chapter-15 | Angles |
| Writer | RS Aggrawal |
| Book Name | Foundation |
| Topics | Solution of Exe-15 A , Exe-15 B |
| Academic Session | 2021-2022 |
Angles Class-6 RS Aggarwal ICSE Maths Goyal Brother Prakashan Chapter-15
–: Select Topics :–
Angles
When two rays begin from the same endpoint then they form an Angle. The two rays are the arms of the angle and the endpoint is the vertex of the angle
Type of Angles
| Acute | An angle which is between 0° and 90° |
| Right | An angle which is exactly equal to 90°. |
| Obtuse | An angle which is between 90° and 180° |
| Reflex | An angle which is between 180° and 360° |
| Straight | An angle which is exactly equal to 180°. |
| Complete | An angle which is exactly equal to 360°. |
Complementary and Supplementary Angles
Complementary Angles are those which have the sum of two angles as 90°.
Supplementary Angles are those which have the sum of two angles as 180°.
There are some special angles (a) 90 (b) 45 (c) 60 (d) 30 (e) 120 (f ) 135 degrees which can be constructed
Constructing a 60º Angle
We know that the angles in an equilateral triangle are all 60º in size. This suggests that to construct a 60º angle we need to construct an equilateral triangle as described below.
Step 1: Draw the arm PQ.
Step 2: Place the point of the compass at P and draw an arc that passes through Q.
Step 3: Place the point of the compass at Q and draw an arc that passes through P. Let this arc cut the arc drawn in Step 2 at R.
Step 4: Join P to R the angle QPR is 60
Constructing a 30º Angle
We know that: Half of 60 is 30
So, to construct an angle of 30º, first construct a 60º angle and then bisect it. Often, we apply the following steps.
Step 1: Draw the arm PQ.
Step 2: Place the point of the compass at P and draw an arc that passes through Q.
Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.
Step 4: With the point of the compass still at Q, draw an arc near T as shown.
Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.
Step 6: Join T to P. The angle QPT is 30º.
Exe-15 A ,
Angles Class-6 RS Aggarwal ICSE Maths Goyal Brother Prakashan Chapter-15
Page 202-203
Question 1:
Name each of the following angles. Also name the vertex and them arms in each case :
Answer :
(i) ∠ABC, vertex is C, arms are CA and CB.
(ii) ∠PTM, vertex is T, arms are TP and TM.
(iii) ∠LSR, vertex is S, arms are SL and SR.
(iv) ∠XZY, vertex is Z, arms are ZX and ZY.
(v) ∠EDF, vertex is D, arms are DE and DF.
(vi) ∠HKG, vertex is K, arms are KH and KG.
Question 2:
How many angles are formed in each of the figure given below ? Name them.
Answer :
(i) In Figure there are Three angles :
∠PQR, ∠QRP, ∠QPR
(ii) In Figure there are Four angles :
∠ABC, ∠BCD, ∠CDA, ∠DAB
(iii) In Figure there are Eight angles :
∠HEF, ∠EFH, ∠EHF, ∠EHG, ∠EFG, ∠HFG, ∠FGH, ∠HGF
Question 3:
Name all possible angles in the figure given below :
Answer :
∠AOB, ∠AOC, ∠AOD, ∠BOC, ∠BOD, ∠COD.
Question 4:
Name the angle shown, using capital letters :
Answer :
∠a = ∠AOB,
∠b = ∠BOP,
∠c = ∠POQ,
∠1 = ∠QOR,
∠2 = ∠ROA
Question 5:
In the adjoining figure ; name the points :
(i) On the angle ;
(ii) In the interior of the angle ;
(iii) In the exterior of the angle.
Answer :
(i) Y, U, P, B, X, O
(ii) A, S, T, Z
(iii) C, R, D, L.
Question 6:
Look at the adjoining figure and state which of the following statements are true and which are false :
(i) Point C in the interior of ∠AOC.
(ii) Point C in the interior of ∠AOD.
(iii) Point D in the interior of ∠AOC.
(iv) Point B in the exterior of ∠AOD.
(v) Point C lies on ∠AOB.
Answer :
(i) False
(ii) True
(iii) False
(iv) True
(v) False
Question 7:
Measure each one of the following angles using protractor :
Answer :
(i) 50°
(ii) 115°
(iii) 50°
(iv) 70°
(v) 75°
(vi) 120°
Exe-15 B,
Angles Class-6 RS Aggarwal ICSE Maths Goyal Brother Prakashan Chapter-15
Page 205
Question 1:
Measure each of the following angles. Write its measure. Write whether it is acute, obtuse, right angle, a straight angle or a reflex angle.
Answer :
(i) 90°, right angle
(ii) 115°, obtuse angle
(iii) 180°, straight angle
(iv) 145°, obtuse angle
(v) 78°, acute angle
(vi) 120°, obtuse angle
Question 2:
Classify the angles whose magnitude are given below :
(i) 93°
(ii) 180°
(iii) 86°
(iv) 125°
(v) 0°
(vi) 90.5°
(vii) 89.5°
(viii) 90°
(ix) 360°
(x) 182°
(xi) 3°
(xii) 25°
Answer :
(i) obtuse angle
(ii) straight angle
(iii) acute angle
(iv) obtuse angle
(v) zero angle
(vi) obtuse angle
(vii) acute angle
(viii) right angle
(ix) complete angle
(x) reflex angle
(xi) acute angle
(xii) acute angle
Question 3:
How many degrees are there in :
(i) one right angle
(ii) two right angles
(iii) three right angles
(iv) 3/5 right angles
(v) 3/2 right angles
(vi) four right angles.
Answer :
(i) 1 x 90° = 90°
(ii) 2 x 90° = 180°
(iii) 3 x 90° = 270°
(iv) 3/5 x 90° = 54°
(v) 3/2 x 90° = 135°
(vi) 4 x 90° = 360°
–: End of Angles Class-6 RS Aggarwal Solutions :–
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