1)how to make 55°,25° only using compass
2)what is definition of regional number
Answers
Answer:
1. (i) Draw a ray OA.
(ii) With O as centre and any suitable radius draw an arc above OA cutting it at a point B.
(iii) With B as centre and the same radius as before, draw another arc to cut the previous arc at C.
(iv) Join OC and produce it to D.
Then ∠AOD = 60°.
2. Construction of an Angle of 120° by using Compass
Step of Construction:
(i) Draw a ray OA.
(ii) With O as centre and any suitable radius draw an arc cutting OA at B.
(iii) With B as centre and the same radius cut the arc at C, then with C as centre and same radius cut the arc at D. Join OD and produce it to E.
Then, ∠AOE = 120°.
3. Construction of an Angle of 30° by using Compass
Step of Construction:
(i) Construction an angle ∠AOD = 60° as shown.
(ii) Draw the bisector OE of ∠AOD.
Then, ∠AOD = 30°.
4. Construction of an Angle of 90° by using Compass
Step of Construction:
(i) Take any ray OA.
(ii) With O as centre and any convenient radius, draw an arc cutting OA at B.
(iii) With B as centre and the same radius, draw an cutting the first arc at C.
(iv) With C as centre and the same radius, cut off an arc cutting again the first arc at D.
(v) With C and D as centre and radius of more than half of CD, draw two arcs cutting each other at E, join OE.
Then, ∠EOA = 90°.
5. Construction of an Angle of 75° by using Compass
Step of Construction:
(i) Take a ray OA.
(ii) With O as centre and any convenient radius, draw an arc cutting OA at C.
(iii) With C as centre and the same radius, draw an cutting the first arc at M.
(iv) With M as centre and the same radius, cut off an arc cutting again the first arc at L.
(v) With L and M as centre and radius of more than half of LM, draw two arcs cutting each other at B, join OB which is making 90°.
(vi) Now with N and M as centres again draw two arcs cutting each other at P.
(vii) Join OP.
Then, ∠POA = 75°.
6. Construction of an Angle of 105° by using Compass
Step of Construction:
(i) After making 90° angle take L and N as centre and draw two arcs cutting each other at S.
(ii) Join SO.
Then, ∠SOA = 105°.
7. Construction of an Angle of 135° by using Compass
Step of Construction:
(i) Construct ∠AOD = 90°
(ii) Produce ∠AO to B.
(iii) Draw OE to bisect ∠DOB.
∠DOE = 45°
∠EOA = 45° + 90° = 135°
Then, ∠EOA = 135°.
8. Construction of an Angle of 150° by using Compass
Step of Construction:
(i) Construct ∠AOC = 120°
(ii) Produce ∠AO to B.
(iii) Draw OD to bisect ∠COB.
Now ∠COD = 30°
Therefore, ∠AOD = 120° + 30° = 150°
Then, ∠AOD = 150°
2. it should be rational number not regional number and the defenation of rational number is that it is a number that can be expressed as a fraction in p/q form and contains integers.