Question

One angle of a triangle is $\frac{2x}{3}$ grad, another is $\frac{3x}{2}$ degrees, whilst the third is $\frac{\pi x}{75}$ radians. Express all angles in degress.

• A. Hence three angles of the triangle are ${43}^{\circ },{30}^{\circ }$ ,${30}^{\circ }$
• B. Hence three angles of the triangle are ${24}^{\circ },{60}^{\circ },$ ${96}^{\circ }$
• C. Hence three angles of the triangle are ${74}^{\circ },{27}^{\circ },$ ${98}^{\circ }$
• D. Hence three angles of the triangle are ${30}^{\circ },{60}^{\circ },$ ${90}^{\circ }$

Answer 1

The correct option is B Hence three angles of the triangle are ${24}^{\circ },{60}^{\circ },$ ${96}^{\circ }$

$\frac{2}{3}{x}^g=\frac{2}{3}x\left(\frac{9}{10}\right)=\frac{3}{5}{x}^{\circ }$
And $\frac{\pi x^c}{75}=\frac{\pi x}{75}\times \frac{{180}^{\circ }}{\pi }=\frac{12x^{\circ }}{5}$
But $\frac{3}{5}{x}^{\circ }+\frac{3}{2}{x}^{\circ }+\frac{12}{5}{x}^{\circ }={180}^{\circ }$
$\therefore 6x^{\circ }+15x^{\circ }+24x^{\circ }=1800$
$45x^{\circ }=1800$
$x={40}^{\circ }$
Hence three angles of the triangle are ${24}^{\circ },{60}^{\circ },$ ${96}^{\circ }$.