Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# One Angle of a Triangle 2 3 X Grades and Another is 3 2 X Degrees While the Third is π X 75 Radians. Express All the Angles in Degrees. - Mathematics

One angle of a triangle $\frac{2}{3}$ 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.

#### Solution

One angle of the triangle = $\frac{2}{3}x \text{ grad }$
$= \left( \frac{2}{3}x \times \frac{9}{10} \right)^\circ\left[ \because 1 \text{ grad }= \left( \frac{9}{10} \right)^\circ\right]$
$= \left( \frac{3}{5}x \right)^\circ$
Another angle = $\left( \frac{3}{2}x \right)^\circ$
$\because 1\text{ radian }= \left( \frac{180}{\pi} \right)^\circ$
$\text{ Third angle of the triangle }= \frac{x\pi}{75}\text{ rad }$
$= \left( \frac{180}{\pi} \times \frac{x\pi}{75} \right)^\circ$
$= \left( \frac{12}{5}x \right)^\circ$
Now,
$\frac{3}{5}x + \frac{3}{2}x + \frac{12}{5}x = 180 \text{ (Angle sum property) }$
$\Rightarrow \frac{6x + 15x + 24x}{10} = 180$
$\Rightarrow \frac{45x}{10} = 180$
$\Rightarrow x = 40$
Thus, the angles are:
$\left( \frac{3}{5}x \right)^\circ= 24^\circ$
$\left( \frac{3}{2}x \right)^\circ = 60^\circ$
$\left( \frac{12x}{5} \right)^\circ= 96^\circ$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 4 Measurement of Angles
Exercise 4.1 | Q 4 | Page 15