1. What is the measure of the angle which is one fifth of its supplementary part?

(a) 15°

(b) 30°

(c) 36°

(d) 75°

2. Consider the following statements:

If a transversal line cuts two parallel lines then

1. Each pair of corresponding angles are equal.

2. Each pair of alternate angles are unequal.

Among these, true statements are–

(a) Only 1

(b) Only 2

(c) both 1 and 2

(d) Neither 1 nor 2

3. If each interior angle of a regular polygon is 144°, then what is the number of sides in the polygon?

(a) 10

(b) 20

(c) 24

(d) 36

4. If sum of external and interior angle at a vertex of a regular polygon is 150°; number of sides in the polygon is

(a) 10

(b) 15

(c) 24

(d) 30

5. If sum of internal angles of a regular polygon is 1080°, then number of sides in the polygon is

(a) 6

(b) 8

(c) 10

(d) 12

6. The ratio of sides of two regular polygon is 1 : 2 and ratio of their internal angle is 2 : 3. What is the number of sides of polygon having more sides?

(a) 4

(b) 8

(c) 6

(d) 12

7. In the two regular polygon number of sides are in the ratio 5 : 4. If difference between their internal angles is 6°, then number of sides in the polygon is

(a) 15, 12

(b) 5, 4

(c) 10, 8

(d) 20, 16

8. If each of interior angle of a polygon in double its each exterior angle, then number of sides in the polygon is

(a) 8

(b) 6

(c) 5

(d) 7

9. Which the following cannot be measure of an interior angle of a regular polygon?

(a) 150°

(b) 105°

(c) 108°

(d) 144°

10. Number of diagonals in a polygon having 10 sides is

(a) 20

(b) 40

(c) 35

(d) 32

Solutions

1. (b); Let required angle be x then its supplementary angle is (180°-x)

According to question,

x=1/5 (180°-x)

5x=180°-x

∴x=(180°)/6=30°

2.(a); Statement (1) is true. Statement (2) is wrong.

3.(a); ∵ Let number of sides be n

According to question, (n-2)180/n=144

(n-2)5=4n

∴ n=10

4. (c); If number of sides in regular polygon be n then

((2n-4))/n×90°-(360°)/n=150°

((2n-4)×3)/n-12/n=5

(6n-12-12)/n=5

6n-24=5n

∴n=24

5. (b); Sum of interior angle of a regular polygon of n sides=(2n-4)×90°

∴(2n-4)×90°=1080°

2n-4=1080÷90=12

2n=12+4=16

∴n=16/2=8

6. (b); Let number of sides in two regular polygon are respectively n and 2n, then their each internal angle are respectively (nπ-2π)/n and (2nπ-2π)/2n

According to question, (((nπ-2π)/n))/(((2nπ-2π)/2n) )=2/3

Or, (n-2)π/(n-1)2π×2=2/3

Or, (n-2)/(n-1)=2/3

Or, 3n-6=2n-2

n=4

∴2n=8

7. (a) Let number of sides be respectively 5x and 4x.

∴ ((2×5x-4)90°)/5x-((2×4x-4)×90°)/4x=6°

[each interior angle=((2n-4)/n)×90°]

(10x-4)×360°-(8x-4)×450°=20x×6°

(10x-4)×12-(8x-4)15=4x

120x-48-120x+60=4x

x=3

∴ Number of sides are respectively 5 and 12.

8. (b); Each internal angle of polygon =[(n-2)180/n]^°

Each exterior angle of polygon=[360/n]^°

According to question,

(n-2)180/n=2×360/n

n-2=4

∴n=6

9. (b); Each interior angle of polygon=(n-2)/n×180°.=60°,

when n=3 ,90°,

when n=4 ,108°,

when n=5,120°,

when n=6 ,135°,

when n=8 ,140°,

when n=9 ,144°

when n=10,150°,

when n=12

10. (c); Since number of diagonals in n sided polygon=n(n-3)/2

For, n=3,

Number of diagonals=(10×7)/2=35

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