Question

Two complementary angles are in the ratio 2 : 3. Find the larger angle between them.

Answer 1

Step-by-step explanation:

2x+3x=90

5x=90

x=18

3x=3×18=54

Answer 2

The larger angle between them is 54°.

• Ratio of two complementary angles is given as 2:3.
• Complementary angles are those angles whose sum is equal to 90°.
• Let us assume the two complementary angles to be x and y.

x + y = 90     ......(Equation 1)

$\frac{x}{y} = \frac{2}{3}$    

3x - 2y = 0    ......(Equation 2)

• Now we solve equation 1 and equation 2
• Multiplying equation 1 by 2 and adding it with equation 2

2x + 2y = 180   ....(Multiplying equation 1 by 2)

3x - 2y = 0      .......(From equation 2)

• Adding both the above equations

5x = 180

x = 36°

• Now substituting the value of x in equation 1

36 + y = 90

y = 54°