1. What is the measure of the angle which is one fifth of its supplementary part?
Ans. (b); Let required angle be x then its supplementary angle is (180°-x)
According to question,
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?
Ans.(a); ∵ Let number of sides be n
According to question, (n-2)180/n=144
4. If sum of external and interior angle at a vertex of a regular polygon is 150°; number of sides in the polygon is
Ans. (c); If number of sides in regular polygon be n then
5. If sum of internal angles of a regular polygon is 1080°, then number of sides in the polygon is
Ans. (b); Sum of interior angle of a regular polygon of n sides=(2n-4)×90°
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?
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
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.
[each interior angle=((2n-4)/n)×90°]
∴ 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
Ans. (b); Each internal angle of polygon =[(n-2)180/n]^°
Each exterior angle of polygon=[360/n]^°
According to question,
9. Which the following cannot be measure of an interior angle of a regular polygon?
Ans. (b); Each interior angle of polygon=(n-2)/n×180°.=60°,
when n=3 ,90°,
when n=4 ,108°,
when n=6 ,135°,
when n=8 ,140°,
when n=9 ,144°
10. Number of diagonals in a polygon having 10 sides is
Ans. (c); Since number of diagonals in n sided polygon=n(n-3)/2
Number of diagonals=(10×7)/2=35