A) Express the following angles in radians
1) 36°
A) π/2 B) π/3 C) π/4 D) π)5
2) 120°
A) π/2 B) 2π/3 C) 3π/4 D) π/5
3) 225°
A) π/2 B) π/3 C) 5π/4 D) π/5
4) 330°
A) 11π/2 B) 11π/3 C) 11π/6 D) π/5
5) 400°
A) π/20 B) 20π/9 C) π/4 D) π/5
6) 7°30'
A) π/24 B) π/3 C) π/4 D) π)/5
7) 22°22'22"
A) π/2 B) π/3 C) π/4 D) π/5 E) n
B) Express the following angles in circular measure.
8) 25ᵍ
A) π/2 B) π/3 C) π/4 D) π/n E) n
9) 22ᵍ 12′ 12′′
A) π/2 B) π/3 C) π/4 D) π/5 E) n
10) 12ᵍ 50′ 30′′
A) π/2 B) π/3 C) π/4 D) π/5 E) n
C) Express the following angles in degree
11) 5π/12
A) 75° B) 648° C) 47°43'38" D) 229 E) n
12) 18π/5
A) 75° B) 648° C) 47°43'38" D) 229 E) n
13) 5/16
A) 75° B) 648° C) 47°43'38" D) 229 E) n
14) -4
A) 75° B) 648° C) 47°43'38" D) 229 E) n
15) The greatest of a triangle are in AP and the greatest angle is double the least. Find all the angles in degrees
A) 40°,60°, 80° B) C) 47°,43°,90° D) 50°, 60°,70° E) n
16) The greatest of a triangle are in AP and the greatest angle is double the least. Find all the angles in degrees.
A) π/3, 2π/9, 4π/9 B) π/2, 2π/9, 4π/9 C) 4π/3, 5π/9, 4π/9 D) n
17) The difference between the two acute angles of a right angled triangle is π/5, find these angles in degrees
A) 63°,27° B) C) 43°,47° D) 50°, 40° E) n
18) The difference between the two acute angles of a right angled triangle is π/5, find these angles in circular measure
A) 7π/20, 3π/20 B) π/2, 2π/9 C) 4π/3, 5π/9 D) n
19) Find the radius of a circle in which a central angles of 45° intercepts an arc of length 33cm (take π= 22/7)
A) 32 B) 42 C) 52 D) 62 E) none
20) Find the length of an arc of a circle of radius 14cm which subtends an angle of 36° at the centre.
A) 6.8 B) 7.8 C) 8.8 D) 9.8 E) n
21) If the arcs of the same length in two circles subtends angles 75° and 120° at the centre, find the ratio of their radii.
A) 8:5 B) 5:8 C) 4:7 D) 8:9 E) n
22) Find the degree measure of the angle subtended at the centre of a circle of diameter 60cm by an arc of length 16.5cm.
A) 31°30' B) 41°30' C) 51°30' D) 61°30" E) n
23) In a circle of diameter 30cm, the length of a chord is 15cm. Find the length of the minor arc of the chord
A)12cm B) 21.7cm C) 15.72cm D) n
24) Find the angle in radians as well as in degrees through which a pendulum swings if its length is 45cm and its tio describes an arc of length 11cm.
A) 11/45, 14° B) 13/45, 45° C) 11/45, 15° D) n
25) The large hand of a clock is 42cm long. How many centimetres does its extremity move in 20mins.
A) 8cm B) 88cm C) 89cm D) n
26) A wheel makes 180 revolutions in 1 minute. Through how many radians does it turns in 1 second?
A) π B) 3π C) 5π D) 6π E) n
27) A train is moving on a circular curve of radius 1500m at the rate of 66km per hour. Through what angle has it turned in 10 seconds
A) 5° B) 6° C) 7° D) 8° E) n
28) The angle A of a parallelogram ABCD is 45º. find the other angle in radian. ∠B=∠D=3πᶜ/4, ∠c=π/4
29) The angles of a triangle are in the ratio 1:4: 5 . find them in centensimal systemt. 20,80,,100
30) 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°
31) 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
32) 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.
A) 88cm B) 99cm C) 11cm D) 22cm E) n
33) Find in sexagesimal measure of each angle of a regular Pentagon.
A) 108° B)72° C) 76° D) 90° E) n
34) 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
35) 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
36) 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
37) 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°
38) 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
39) 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°
40) 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°
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