Question

solve question 17 please,

Answer 1

Answer:

e) 30°

[ The correct answer isn't one of the options! ]

Step-by-step explanation:

First, let's eliminate the answers that are there.  Then we'll get the correct answer.

a) 15°  Its supplement is 180° - 15° = 165°.   15° is not one-fifth of 165°.

b) 36°  Its supplement is 180° - 36° = 144°.   36° is not one-fifth of 144°.

c) 75°  Its supplement is 180° - 75° = 105°.   75° is not one-fifth of 105°.

d) 150°  Its supplement is 180° - 150° = 30°.   150° is not one-fifth of 30°.

So none of the answers is correct!  However, notice that in (d), 150° has the property that its supplement is one-fifth of it, so maybe this is what the question writer intended, but they made a mistake.

The correct answer

We've already seen that 30° is the answer, as it is one-fifth of its supplement which is 150°.  However, let's see how we would have worked that out.

Let x be the degree measure of the angle.

Its supplement is then 180 - x degrees.

So:

   the angle equals one-fifth of its supplement

=> x = ( 180 - x ) / 5

=> 5x = 180 - x

=> 6x = 180

=> x = 30