Question

in a right angle triangle the difference between two acute angle is pi by 18 in radian measure Express the angles in degrees.​

Answer 1

Answer:

50° and 40°

Step-by-step explanation:

[Please refer the image attached for figure]

In figure, we have ΔABC with acute angles x and y.

According to question, let :

x - y = $\frac{\pi }{18}$ rad

To convert radian --> degree measure, formula is :

Degree measure = $\frac{180}{\pi }$ × Radian measure

So, corresponding degree measure of $\frac{\pi }{18}$ rad is :

= $\frac{180}{\pi }$ × $\frac{\pi }{18}$  = 10°

Then we can rewrite the above equation as :

x - y = 10°

=> x = y + 10°

Hence the two acute angles become [y + 10]° and y° resp.

Now by angle sum formula,

∠A + ∠B + ∠C = 180°

=> y + 90° + [y + 10] = 180°

=> 2y + 100 = 180

=> 2y = 80

=> y = 40°

From our first equation,

x - y = 10°

Substitute y = 40°

x - 40 = 10

=> x = 40 + 10

=> x = 50°