# The Difference Between the Two Acute Angles of a Right-angled Triangle is 2 π 5 Radians. Express the Angles in Degrees. - Mathematics

The difference between the two acute angles of a right-angled triangle is $\frac{2\pi}{5}$ radians. Express the angles in degrees.

#### Solution

Given:
Difference between two acute angles of a right-angled triangle = $\frac{2\pi}{5}$ rad  $\because 1 \text{ rad }= \left( \frac{180}{\pi} \right)^\circ$
$\therefore \frac{2\pi}{5} rad = \left( \frac{180}{\pi} \times \frac{2\pi}{5} \right)^\circ$
$= \left( 36 \times 2 \right)^\circ$
$= {72}^\circ$
Now, let one acute angle of the triangle be x°.
Therefore, the other acute angle will be 90° - x°.
Now,
$x^\circ - \left( 90^\circ - x^\circ \right) = 72^\circ$
$\Rightarrow x - 90 + x = 72$
$\Rightarrow 2x = 162$
$\Rightarrow x = 81$
Thus, we have: x° = 81 and,
90° - x°
= 90° - 81°
=9°

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 4 Measurement of Angles
Exercise 4.1 | Q 3 | Page 15