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

(a) 15°

**(b) 30°**

(c) 36°

(d) 75°

**Ans. (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. 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

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

**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

**Ans.(a); ∵ Let number of sides be n**

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

**(n-2)5=4n**

**∴ n=10**

**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

**Ans. (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. 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

**Ans. (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. 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

**Ans. (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. 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

**Ans. (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. 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

**Ans. (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. Which the following cannot be measure of an interior angle of a regular polygon?**

(a) 150°

**(b) 105°**

(c) 108°

(d) 144°

**Ans. (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. Number of diagonals in a polygon having 10 sides is**

(a) 20

(b) 40

**(c) 35**

(d) 32

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

**For, n=3,**

**Number of diagonals=(10×7)/2=35**