Math Practice SET 6

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