Question

Solve the following problems using two variables.
(i) In a right angled triangle , one of the acute angle exceeds the other by 20^o.
Find the measure of both the acute angles in the right angled triangle.

Answer 1

Let the smaller acute angle in the right angled triangle be x and the greater acute be y.
Then we have:
x + y + 90^o = 180^o (Angle sum property)
⇒ x + y = 180^o $-$ 90^o
⇒ x + y = 90^o ...(1)
and
x + 20^o = y
⇒ x $-$ y = $-$ 20^o ...(2)
Adding equation (1) and (2), we get:
x + y = 90^o
x $-$ y = $-$ 20^o
---------------------
2x = 70^o
⇒ x = 35^o
Substituting the value of x in equation (1), we get:
35^o + y = 90^o
⇒ y = 55^o
∴ The acute angles of the right angled triangle are 35^o and 55^o.