Question

One angle of a triangle is $\frac{2}{3}x$ grades and another is $\frac{3}{2}x$ degrees while the third is $\frac{\pi x}{75}$ radians. Express all the angles in degrees.

Answer 1

Let ${\theta }_{1}and{\theta }_{2}and{\theta }_3$ be the angle or triangle.

${\theta }_1=\frac{2}{3}x$ gradiants

${\theta }_2=\frac{3}{2}x$ degrees and

${\theta }_3=\frac{\pi x}{75}x\times$ radians

Now,

We have to express all the angles in degrees

$\therefore {\theta }_1={(\frac{3}{2}x\times \frac{90}{100})}^{\circ }$

$=\frac{3}{5}x[1g=\frac{90}{100}\text{degree}]$

${\theta }_2=\frac{3}{2}{x}^{\circ }$

${\theta }_2=\frac{\pi x}{75}\times \frac{180}{\pi }=\frac{12x}{5}$

By angleslam property,

${\theta }_1+{\theta }_2+{\theta }_3={180}^{\circ }$

$\therefore \frac{3}{5}{x}^{\circ }+\frac{3}{2}{x}^{\circ }+\frac{12x}{5}={180}^{\circ }$

$\Rightarrow \frac{9}{2}{x}^{\circ }={180}^{\circ }$ $\Rightarrow x={40}^{\circ }$

$\therefore {\theta }_1={24}^{\circ },{\theta }_2={60}^{\circ },{\theta }_3={96}^{\circ }$