Measurement of angle (XI)

 MEASUREMENT OF ANGLE

1) Express the following angles  in both Centesimal and circular measure.

a) 30°

b) 15° 15' 15"

c) 40° 20"

2) Express the following angles in both sexagesimal and circular measure.

a)  25ᵍ

b) 22ᵍ 12′ 12′′

c) 12ᵍ 50′ 30′′ 

3) Express the following angles in in both sexagesimal and centesimal measure.

a) 14π/15

b)  7π/9

c) 5π/10

4) The angle A of a parallelogram ABCD is 45º. find the other angle in radian.   ∠B=∠D=3πᶜ/4, ∠c=π/4

5)  The angles of a triangle are in the ratio 1:4: 5 . find them in centensimal systemt.   20,80,,100

6) The Vertical angle of an isosceles triangle is three times the sum of of the base angles. find the angles in sexagesimal system.                                       20°30',22°30',135°

7) The length of a big hand of a clock is 20cm. How much will its extremity move in 20 minutes ?find also the area swept by the hand in that time.          27.94m,139.68cm²

8) The circumference of the dial of a clock is a 44cm. How far does the tip of the big hand move from 3 p.m. to 5-15 p.m.                   99cm

9) Find in sexagesimal measure of each angle of a regular Pentagon.                                                      108°

10) The sum of two angles is equal to 112°. If the number of grade in one is one is twice the number of degrees in the other, find the angle in grades.                        80, 44.44

11) Two circles are such that two arcs of equal lengh subtend 18° and 24°at the respective centre. if the radius of the the first circle is 3 cm, find that of the other.       2.25

12) Two circle are such that their radius are in the ratio 2:3. Find the ratio of the length of to arc which subtend which subtend at the centre of the respective circle angles in the ratio 4:5.          8:15

13) The angles of a quadrilateral are in AP and the ratio of the least angle in degrees and the greatest angle in Radian IS 90:π. Find the least angle in degreess.          60°

14) The distance of the sun from the earth is 149.5x 10⁶ Km and the angle subtended by the sun at a point on the earth is half a degree. find the approximate diameter of the Sun. (π=22/7).     1305159 km

15) A wire in the form of a square of each side 4cm is the bent to form a circular arc of radius 6cm. Find the angle made by that are at the centre.(π=22/7).                 152.7°

16) A boy in a Merry Go Round of a diameter 10 m is revolving about the centre at a speed of 100m per hour. Find in degrees the angle turned by the boy in one minute                                                          19.1°