Question

If $D,G$ and $R$ denote respectively the number of degrees, grades and radians in an angle, then

• A. $\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }$
• B. $\frac{D}{90}=\frac{G}{100}=\frac{R}{\pi }$
• C. $\frac{D}{100}=\frac{G}{90}=\frac{2R}{\pi }$
• D. $\frac{D}{90}=\frac{G}{100}=\frac{R}{2\pi }$

Answer 1

The correct option is A $\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }$

We know, ${90}^{\circ }=1$ right angle.

$\Rightarrow 1^{\circ }=\frac{1}{90}$ right angle

$\Rightarrow D^{\circ }=\frac{D}{90}$ right angle

$\therefore \theta =\frac{D}{90}$ right angle ....(1)

Now,
${100}^g=1$ right angle.

$1^g=\frac{1}{100}$ right angle

$\Rightarrow G^g=\frac{G}{100}$ right angle

$\therefore \theta =\frac{G}{100}$ right angle .....(2)

We also know,

$\pi$ radians = 2 right angle

$\Rightarrow$ 1 radian $=\frac{2}{\pi }$ right angle

$\Rightarrow$ R radian $=\frac{2R}{\pi }$ right angle

$\therefore \theta =\frac{2R}{\pi }$ right angle ...(3)

From, (1), (2) and (3), we get

$\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }$

Hence, the correct option is (C).