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Answers
Answer:
31.(i)L. H. S= -½-4/3+3/7
= -1(21)-4(14)+3(6)/42
=-21-56+18/42
= -59/42
R. H. S= -1/2+3/7-4/3
= -1(21)+3(6)-4(14)/42
=-21+18-56/42
=-59/42
L. H. S=R.H.S
hence. proved
(ii) L. H. S= 2/3*(-6/7+4/5)
= 2/3(-6(5) +4(7) /35)
= 2/3(-11+28/35)
= 2/3(17/35)
= 34/105
R. H. S = (2/3*4/5) *(-6/7)
= 8/15*-6/7
= -48/105
L. H. S is not equal to R. H. S
32.5/22+3/7-8/21-6/11
= { 5(21) +3(66) -8(22) -6(42) } /462
= 105+198-176-252/462
= -125/462
33. (-14*3*-4*15) / (9*5*7*16)
= 2520/5040
=0.5
34. multiplying 3/7*3/3=9/21
multiplying 2/3*7/7=14/21
As denominator are now same, the numerator values between 9 and 14 will lie between these two rational numbers. So the numbers lies between 3/7 and 2/3 are 10/21, 11/21, 12/21 and 13/21.
35. multiplying 1/4*10/10=10/40
multiplying 2/5*8/8=16/40
11/40, 12/40, 13/40, 14/40, 15/40 are required rationals
36. multiplying -2/3 *3/3=-6/9
multiplying 2/3 *3/3=6/9
-5/9, -4/9, -3/9, -2/9, -1/9, 0/9, 1/9, 2/9, 3/9 , 4/9, 5/9 are required rationals
37. A =-3/13; B = -7/13 ; C= -10/13
38. required rational = x
x= -28/81÷-2/3
= -28/81*3/2
= -84/-162
=84/162
39. let the whole =x
1x+2x+3x+4x=360
10x=360
x=360/10
x=36
1x=36
2x=36*2=72
3x=36*3=108
4x=36*4=144
40. Each interior angle of the polygon is 108 degrees, so each exterior angle of the polygon is 180-108 = 72 degrees. So the number of sides is 360/72 = 5. Hence it is a regular pentagon.
41. Number of sides is 12.
Sum of interior angle and exterior angle of a polygon is 180 degree.
Let exterior angle is x.
Interior angle is 5x.
x + 5x = [math]180°[/math]
[math]x = 30°[/math]
Sum of all exterior angles of a polygon is 360 degree
So n X x = [math]360°[/math]
n = [math] 360°/30°[/math]
n=12
42. let, the whole =x
4x+5x=180
9x=180
x=180/9
x=20
4x= 20*4=80
5x=20*5=180
43. Since the sum of all the exterior angles of a convex polygon is always = 360 degrees, it follows that by adding up all the 45 degree exterior angles, one must get a total = 360. (i.e. 45 * n =360, where n= the number of sides of the polygon). Dividing both sides of the equation by 45 gives the answer: n = 8. The figure has eight sides -- it's an octagon.
44. A 162° interior angle at each vertex means that the deflection angle (the amount by which the next side deflects from the course of the current side) is 180°-162°=18°. Since deflecting 360° takes you back to where you started, the number of sides is given by:
n = 360°/DeflectionPerVertex = 360°/18° = 20.
Hence the polygon has 20 sides and 20 vertices
45. Each triangle has an angle sum of 180 degrees, so the sum of the interior angles of the 15-gon must be 13 × 180 = 2340 degrees. Since the 15-gon is regular, this total is shared equally among the 15 interior angles. Each interior angle must have a measure of 2340 ÷ 15 = 156 degrees.
46. opposite angles of parallelogram are equal so, two angles measure 70° each
adjacent angles are supplementary so, other two angles measure 110°(180-70) each
70,110,70,110 are angles of given parallelogram
47. 111+x+x+x=360
111+3x=360
3x=360-111
3x=249
x=249/3
the tree angles measure =x= 83°
48. 3/8
the ratio of the sum of the interior angles of a pentagon to the sum of the interior angles of a decagon is (3 * 180) / (8 * 180). this results in 3/8.
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