Given the numbers of sexagesimal and centesimal minutes of any angle, you need to prove that:
[tex]\frac{M_1}{27}=\frac{M_2}{50}[/tex]
By definition, a Right Angle measures 90 degrees.
By definition, for Sexagesimal:
[tex]1\text{\degree}=60\text{ }minutes[/tex][tex]1\text{ }minute=60\text{ }seconds[/tex]
Then, in the sexagesimal form, a Right Angle is:
[tex]90\cdot60\cdot60\text{ }seconds[/tex]
By definition, for Centesimal:
[tex]90\text{\degree}=100\text{ }g[/tex][tex]100\text{ }g=100\text{ }minutes[/tex][tex]1\text{ }minute=100\text{ }seconds[/tex]
Therefore, a Right Angle is:
[tex]100\cdot100\cdot100\text{ }seconds[/tex]
So you can set up this ratio:
[tex]\frac{M_1}{M_2}=\frac{90\cdot60}{100\cdot100}[/tex]
Simplifying, you get:
[tex]\frac{M_1}{M_2}=\frac{27}{50}[/tex]
Hence, the answer is:
[tex]\frac{M_1}{M_2}=\frac{90\cdot60}{100\cdot100}[/tex][tex]\frac{M_1}{M_2}=\frac{27}{50}[/tex]
Therefore:
[tex]\frac{M_1}{27}=\frac{M_2}{50}[/tex]
