# Convert the Systems of Measuring Angles

To convert the systems of measuring angles from one system to the other system.

1. Convert  63°14’51” into circular measure.

Solution:

63°14'51"

= 25299/(400 × 90) Right angle

= 2811/4000 Right angle

= (2811π/8000)c

2. Convert 100g45’24” in right angles.

Solution:

100g45'24"

= 100g + 4524/100)"

= 100g + (4524/100)'

= 100g + {4524/(100 × 100)}g

= 100g + (4524/10000)g

= (1001131/2500)g

= (251131/2500)g

= (251131/2500 × 100) Right angles

= (251131/250000) Right angles

= 11131/250000 Right angles

3. Convert  63°14'51" into centesimal measure.

Solution:

63°14'51"

= 63° + (1451/60) [Since, 1' = 60"]

= 63°+ (297/20)'

= {63297/(20 × 60)}° [Since, 60' = 1°]

= (25299/400)°

= {25299/(400 × 90)} Right angle [Since, 90° = 1 Right angle]

= [{25299/(400 × 90)} × 100]g, [Since, 100g = 1 Right angle]

= 70g + {(11/40) × 100}, [Since, 1g = 100']

= 70g + (271/2)‵

= 70g 27‵50‶, [Since, 1‵ = 100‶]

4. Convert  145°10'48"  in right angles

Solution:

145°10'48"

= 145° + (1048/60)' [Since, 60" = 1']

= 145° + (54/5)'

= 145° + {54/(5 × 60)}° [Since, 60' = 1°]

= 145° + (9/50)°

= (7259/50)°

= 7259/(50 × 90) Right angles

= 12759/4500 Right angles

Measurement of Angles

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