Measurement of Angle_Questions

Short Questions:

1. Convert into sexagesimal seconds.
   1. 20°
   2. 60°
   3. 25° 15'
   4. 40° 40' 20"
   5. 120° 20' 20"
2. Convert into centesimal seconds.
   1. 15°
   2. 20°
   3. 25° 25'
   4. 10° 20' 10"
   5. 20° 20' 20"
3. Convert into grades.
   1. 63°
   2. 27°
   3. 54°
   4. 144°
   5. 126°
4. Convert into degrees.
   1. 40°
   2. 63°
   3. 120°
   4. 117°
5. Convert into degrees.
   1. 45° 30'
   2. 60° 45'
   3. 20° 30' 25"
   4. 54° 12' 15"
6. Convert into grades.
   1. 40° 45'
   2. 50° 15'
   3. 70° 50' 25"
   4. 80° 75' 75"
7. Convert into radians.
   1. 40°
   2. 90°
   3. 75°
   4. 120°
   5. 54°
8. Convert into degrees.
   1. (\(\frac{\pi}{4}\))°c
   2. (\(\frac{\pi}{9}\))°c
   3. (\(\frac{3\pi}{4}\))°c
   4. (\(\frac{4\pi}{5}\))°c
   5. (\(\frac{7\pi}{4}\))°c

9. Convert into radians.

   1. 50°
   2. 80°
   3. 75°
   4. 120°
   5. 150°

10. Convert into grades.

    1. (\(\frac{3\pi}{5}\))°c
    2. (\(\frac{\pi}{20}\))°c
    3. (\(\frac{3\pi}{10}\))°c
    4. (\(\frac{2\pi}{5}\))°c
    5. (\(\frac{7\pi}{10}\))°c

11. Find the remaining angle in stated units.

    1. One angle of a right-angled triangle is 70°. Find the remaining angle in grades.
    2. One angle of a right-angled triangle is 72°. Find the remaining angle in radian measure.
12. The angles of a triangle are in the ratio 3 : 4 : 3. Find all the angles in
    1. degrees
    2. grades
    3. radians.
13. The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 1. Find all the angles in
    1. degrees
    2. grades
    3. radians
14. The two angles of a triangle are in the ratio 4 : 5 and the third angle is 90°. Find all the angles in grades.
15. If two angles of a triangle are 45° and (\(\frac{\pi}{6}\))°c, find the remaining angle in degree.
16. If one angle of an right-angled triangle is 25°, find the remaining angle in radian measure.
17. Two acute angles of a right angled triangle are 63° and 30°. Express all angles in radian.
18. If D and G are the number of degrees and grades of the same angle, prove that \(\frac{G}{10} = \frac{D}{9}\).
19. If M and m represents the number of sexagesimal and centesimal minute of any angle respectively, prove that \(\frac{M}{27} = \frac{m}{50}\)