Question

Let x represent the measurement of an acute angle in degrees. The ratio of the complement of x to the supplement of c is 2:5. Guess and check to determine the value of x. Explain why your answer is correct.

Answer 1

Answer:

The ratio of the complement of x to the supplement of x is 2:5. The value of x is 30

Solution:

It is given that x represents the measurement of an acute angle in degrees.  It is also given that the ratio of the complement of x to the supplement of x is 2:5.  

Since it is given that x is an acute angle it means that it has to be less than 90.

Complement of an angle = 90 - x

Supplement of an angle = 180 - x

In this case it is given that the ratio of the complement of x to the supplement of x is 2:5

So we can write the relation as follows:

$\begin{array}{l}{\frac{90-x}{180-x}=\frac{2}{5}} \\\\ {(90-x) \times 5=(180-x) \times 2} \\\\ {450-5 x=360-x) \times 2} \\\\ {450-560=5 x-2 x} \\\\ {90=3 x} \\\\ {x=\frac{90}{3}=30}\end{array}$

Therefore the value of x is 30.