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

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}{(90-x)/(180-x)=(2)/(5)} \\\\ {(90-x) * 5=(180-x) * 2} \\\\ {450-5 x=360-x) * 2} \\\\ {450-560=5 x-2 x} \\\\ {90=3 x} \\\\ {x=(90)/(3)=30}\end{array}`

Therefore the value of x is 30.