Question

An angle is 1/4 of its complement.What is its magnitude?

Answer 1

$\boxed{\boxed{\large\mathbf{18 ; 72}}}$

_____________________

Let the common ratio be x

Then the angles are $\mathsf{x ; \frac{1}{4} x}$

_____________________

We know that,

Sum of Complementary Angles = 90°

_____________________

$\mathsf{=> x + \frac{1}{4}x = 90}$

$\mathsf{=> \frac{4 + 1}{4}x = 90}$

$\mathsf{=> \frac{5}{4}x = 90}$

$\mathsf{=> x = \frac{90 \times 4}{5}}$

$\mathsf{=> x = 18 \times 4}$

$=>\boxed{\mathbf{ x = 72}}$

$\mathsf{\frac{1}{4}x => \frac{1}{4} \times 72}$

$=> \boxed{\mathsf{ \frac{1}{4}x = 18}}$

Hence, the measure of complmentary angles is 18° and 72°    

Answer 2

Answer:

this is the right way to answer this question