Question

The diagram shows triangle ABC. Angel ABC is NOT an obtuse angle. Find the greatest value of x. You must show all your working. (Your final line should say ‘Greatest value of x is..’)

Answer 1

First, an angle in a triangle is always less than 180.

An obtuse angle is defined to be greater than a right angle, but less than 180. Since angle ABC is not an obtuse angle, its measurement must be 90 degrees or less.

Angle ABC = x + 3x + 30 = 4x + 30
Since we want x to has its greatest value, angle ABC must also have its greatest value ( -> 90)

Now, we find x : (90-30)/4 = 15

So, the greatest value of x is 15. (recheck : 15 + 15 x 3 + 30 = 90)