Question

Express the sexagesimal measure ${135}^{\circ }$ as centesimal measure

Answer 1

Given: $D=135$

To convert sexagesimal measure into centesimal measure and vise versa,

Since, $1\text{right angle}={90}^{\circ }\text{or}{100}^g$

$\Rightarrow 1^{\circ }=(\frac{100}{90}{)}^g$

$\Rightarrow {135}^{\circ }=(135\times \frac{100}{90}{)}^g$

$\Rightarrow {135}^{\circ }=(15\times 10{)}^g$

$\Rightarrow {135}^{\circ }={150}^g$

(or)

Use the formula $\frac{D}{90}=\frac{G}{100}$

$\Rightarrow \frac{135}{90}=\frac{G}{100}$

$\Rightarrow \frac{3}{2}=\frac{G}{100}$

$\Rightarrow G=\frac{300}{2}={150}^g$