Download SA - GEOMETRY-POLYGONS TIME LIMIT – 6 MINS

SA - GEOMETRY-POLYGONS
TIME LIMIT – 6 MINS
PUBLISHED DATE – 27-04-2016
1.
2.
3.
4.
5.
In a regular polygon, the exterior and interior angles
are in the ratio 1 : 4. The number of sides of the
polygon is
(a)5
(b)10
(c)3
(d)8
The difference between the interior and exterior
angles at a vertex of a regular polygon is 150°. The
number of sides of the polygon is
(a) 10
(b) 15
(c) 24
(d) 30
Each interior angles of a regular polygon is 144°. The
number of sides of the polygon is
(a) 8
(b) 9
(c) 10
(d) 11
If the sum of the interior angles of a regular polygon
be 1080°, the number of sides of the polygon is
(a) 6
(b) 8
(c) 10
(d) 12
The number of sides in two regular polygons are in the
ratio of 5 : 4. The difference between their interior
angles of the polygon is 6°. Then the number of sides
are
(a) 15, 12
(b) 5,4
(c) 10, 8
(d) 20, 16
6.
Each internal angle of regular polygon is two times its
external angle. Then the number of sides of the
polygon is:
(a) 8
(b) 6
(c) 5
(d) 7
7. Ratio of the number of sides of two regular polygons is
5 : 6 and the ratio of their each interior angle is 24 : 25.
Then the number of sides of these two polygons are
(a) 10, 12
(b) 20, 24
(c) 15, 18
(d) 35, 42
8. Measure of each interior angle of a regular polygon
can never be:
(a) 150°
(b) 105°
(c) 108°
(d) 44°
9. Each interior angle of a regular polygon is three times
its exterior angle, then the number of sides of the
regular polygon is:
(a) 9
(b) 8
(c) 10
(d) 7
10. The ratio between the number of sides of two regular
polygons is 1 : 2 and the ratio between there interior
angles is 2 : 3. The number of sides of these polygons
is respectively
(a) 6, 12
(b) 5, 10
(c) 4, 8
(d) 7, 14
1.
(b)Interior angle + Exterior Angle = 180°
4𝑥 + 𝑥 = 180
𝑥 = 36
So, No. of sides =
2.
3.
4.
5.
360 °
=
Exterior angle
360
36
= 10
(c)Interior angle – Exterior angle = 150 ………….(i)
Interior angle + Exterior angle = 180 …………(ii)
Interior angle = 165°
Exterior angle = 15°
360
So, No. of sides =
= 24
15
(c)Exterior angle = 180° − 144° = 36°
360
No. of sides = 36 = 10
(b)Sum of interior angle = (𝑛 − 2) × 180
(𝑛 − 2) × 180 = 1080
108
(𝑛 − 2) =
18
𝑛=8
(a)A.T.Q.
180 −
6.
360
360
− 180 −
= 6°
5𝑥
4𝑥
𝑥=3
So, No. of sides = 15, 12
(b) 2𝑥 + 𝑥 = 180
𝑥 = 60°
No. of sides =
7.
360
60
=6
(a)Each interior angle =
So,
(𝑛 1 −2)×180
𝑛1
(𝑛 2 −2)×180
𝑛2
(2𝑛−4)×90
𝑛
𝑛1 5𝑥
=
𝑛2 6𝑥
24
= 25
5𝑥−2
⇒
5𝑥
6𝑥−2
6𝑥
=
24
⇒𝑥=2
25
⇒ No. of sides = 5 × 2 = 10
6 × 2 = 12
8.
(b) Interior angle =
Using options–
(b)
(2𝑛−4)×90
𝑛
= 180 −
360
𝑛
105° = 180° −
9.
which is impossible.
(b) 3𝑥 + 𝑥 = 180
360°
24
⇒𝑛=
𝑛
5
𝑥 = 45°
No. of sides =
10. (c) A. T. Q –
360
𝑛1
360
180 −
𝑛2
180 −
360
45
2 𝑛
=8
𝑥
= 3 , 𝑛 1 = 2𝑥
2
𝑥=4
So, sides = 4, 8