Question

find the measure of the angle which is 1/4 times it's complementary angle ?​

Answer 1

Solution:-

Let the the larger angle be " x "

$\implies \: x + \dfrac{1}{4} = 90$

( Complementary angle measures 90° )

$\implies \: \dfrac{x}{1} + \dfrac{1}{4} = 90$

$\implies \: = \dfrac{(4 \times x) + (1 \times 1)}{4}$

$\implies \: \dfrac{4x + 1}{4} = 90$

$\implies \: 4x + 1 = 90 \times 4$

$\implies \: 5x = 360$

$\implies \: x = \dfrac{360}{5}$

$\implies \: x = 72$

∴ The larger angle is 72°

The other angle is

⟹ 90 - 72

⟹ 18°

∴ The smaller angle is 18°

Now, Verification

⟹ 72 + 18 = 90

⟹ 90 = 90

L.H.S = R.H.S

Hence, Proved

Required Answer:-

• The angles are 72° and 18°