Question

The angle measuring \[\dfrac{{{\pi ^c}}}{4}\] when expressed in centesimal system is
1) \[{50^g}\]
2) \[{60^g}\]
3) \[{75^g}\]
4) \[{100^g}\]

Answer 1

Hint: Here, we will rewrite the angle in terms of degree. Then we will use the equation, \[90^\circ = {10^g}\] to convert the given angle in grades using the centesimal system.

Complete step-by-step answer:
Given that the angle measures \[\dfrac{{{\pi ^c}}}{4}\].

We know that in a centesimal system, as the angle is measured in grades, minutes and seconds.

We can rewrite the given angle \[\dfrac{{{\pi ^c}}}{4}\].

\[
   \Rightarrow \dfrac{{{\pi ^c}}}{4} = \dfrac{{180^\circ }}{4} \\
   \Rightarrow \dfrac{{{\pi ^c}}}{4} = 45^\circ {\text{ ......}}\left( 1 \right) \\
\]

Since we know that one right angle is \[{100^g}\].
Thus, \[90^\circ = {100^g}\].

We will find the value of \[1^\circ \] in the above equation.

\[
   \Rightarrow 1^\circ = {\left( {\dfrac{{100}}{{90}}} \right)^g} \\
   \Rightarrow 1^\circ = {\left( {\dfrac{{10}}{9}} \right)^g} \\
\]

Using this value of \[1^\circ \] in \[\left( 1 \right)\], we get

\[
   \Rightarrow 45^\circ = \dfrac{{10}}{9} \times {45^g} \\
   \Rightarrow 45^\circ = {50^g} \\
\]
Thus, we have found out that the angle measuring \[\dfrac{{{\pi ^c}}}{4}\] when expressed in the centesimal system is \[{50^g}\].
Hence, option A is correct.

Note: Many times students don’t know about the centesimal system and skip the major value, \[90^\circ = {10^g}\]and calculate the wrong solution. Also, many students don’t know about the conversion of angles into grades, thus it is recommended to learn to convert angles into grades.