3. In a right angled triangle, one of the acute angle exceeds the other by 20º. Find the measure of both the acute angles in the right angled triangle.

Solution:

Let the measures of two acute angles of a right angled triangle be xº and yº.

As per the given condition,

x = y + 20

∴  x – y = 20 ....... eq. no. (1)

We know, x + y = 90 ...... eq. no. (2)

[Acute angles of a right angled triangle are complementary]

Adding (1) and (2),

x – y = 20

x + y = 90

2x     =  110

∴ x = 110/2

∴ x = 55

Substituting x = 55 in (2),

55 + y = 90

∴  y = 90 – 55

∴  y = 35

∴  The measures of the two acute angles of a right angled triangle are 55º and 35º.