= (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