= (30 × 3600)" + (30 × 60)" + 30"

= 108000" + 1800" + 30"

= 109830"

= 18° + (\(\frac{30}{60}\))° + (\(\frac{15}{60×60}\))°

= 18°+ (\(\frac{30}{60}\))°+ (\(\frac{15}{3600}\))°

= (\(\frac{18×3600 + 60×30 + 15}{3600}\))°

= (\(\frac{66615}{3600}\))°

= 18.5042°

= (50 × 10000)" + (49 × 100)" + 38"

= 500000" + 4900" 38"

= 504938"

= 50g + (\(\frac{87}{100}\))g + (\(\frac{50}{100×100}\))g

= 50g + (\(\frac{87}{100}\))g + (\(\frac{50}{10000}\))g

= 50g + 0.87g + 0.005g

= (50+0.87+0.005)g

= 50.875g

Here,

x = 72°

we have,

or, x° = (\(\frac{10}{9}×x\))g

or, 72° = (\(\frac{10}{9}×72\))g

∴ 72° = 80g

Here,

or, x = 60°

we have,

or, xg= (\(\frac{9}{10}×x\))°

or, 60g = (\(\frac{9}{10}×60\))°

∴, 54°

Here,

or, x = 60°

we have,

or, x° = (\(\frac{π}{180}×x\))c

or, 60° = (\(\frac{π}{180}×60\))c

= \(\frac{π^c}{3}\)

Here,

or, x = 75g

we have,

or, x° = (\(\frac{π}{200}×x\))c

∴, 75g=(\(\frac{π}{200}×75\))c

= \(\frac{3π^c}{8}\)

Here,

or, x = \(\frac{2π^c}{5}\)

we have,

or, xc = (\(\frac{180}{π}×x\))°

∴ \(\frac{2π^c}{5}\) = (\(\frac{180}{π}\) × \(\frac{2π}{5}\))°

= 72°

Here,

or, x = \(\frac{4π^c}{5}\)

we have,

or, xc = (\(\frac{200}{π}×x\))g

∴ \(\frac{4π^c}{5}\) = (\(\frac{200}{π}\) ×\(\frac{4π}{5}\))g

= 160g

or, 27° 30' = 27° + (\(\frac{30}{60}\))°

= 27° + (\(\frac{1}{2}\))°

= (\(\frac{55}{2}\))°

∴ 27° 30' = (\(\frac{55}{2}\) × \(\frac{10}{9}\))g

= (\(\frac{275}{9}\))g

Here,

or, 42g60' = 42g+ (\(\frac{60}{100}\))g

= 42g+ (\(\frac{3}{5}\))g

= (42.6)g

= (\(42.6 × \frac{9}{10}\))°

= 38.34°

Here,

\(\angle\)A = 60°, \(\angle\)B = 90°

Now,

\(\angle\)A + \(\angle\)B + \(\angle\)C = 180°

or, 60° + 90° + \(\angle\)C = 180°

or, \(\angle\)C = 180° − 150°

or, \(\angle\)C = 30°

Then,

or, 1° = (\(\frac{10}{9}\))g

or, \(\angle\)A = 60° = (\(60×\frac{10}{9}\))g = (\(\frac{200}{3}\))g

or, \(\angle\)B = 90° = (\(90×\frac{10}{9}\))g = 100g

or, \(\angle\)C = 30° = (\(30×\frac{10}{9}\))g = (\(\frac{100}{3}\))g

solution:

In 60 minutes, the minutes hand makes 360°

In 1 minute, the minute hand makes (\(\frac{360}{60}\))°In 15 minutes, the minute hand makes (\(\frac{360×15}{60}\))° = 90°

Hence, a minute hand makes 90° in 15 minutes.

Solution:

Here,
x = 100
we have,
or, xg = (\(\frac{π}{200} × x \))c
or, 100g= (\(\frac{π}{200} × 100 \))c
∴ 100g= (\(\frac{π}{2}\))c