The two angles of a right angled triangle other than . . .

Question : The two angles of a right angled triangle other than 90° are in the ratio 2:3. Express the given situation algebraically as a system of linear equations in two variables and hence solve it. 

CBSE 2025

Solution : 

Let the measures of the two angles be x and y. 

ATQ
x+y+90°=180° (ASP)
x+y=180°-90°
x+y=90° — (1) 

Also 
x:y=2:3
x/y=2/3
3x=2y
3x-2y=0 — (2) 

Solving equation (1) and (2) 

[x+y=90°]×2

[3x-2y=0]×1

2x+2y=180°
3x-2y=0
----------------
5x+0y=180
----------------

5x=180
x=180/5
x=36°

putting in equation (1)

36°+y=90°
y=90°-36°
y=54°

Hence, the required values of two angles is 36° and 54°.