Question

The measurement of the angle K is 3x - 42, and it is obtuse. Find the restriction(s) on the values of x.

Answer 1

x = 44° and 74°: x cannot be less than 44°, x cannot be greater than 74°.

Explanation:

Obtuse angles are greater than 90° but less than 180°.

We can first solve for the lower bound of x.

• 
  `3x-42=90`
• 
  `3x=132\\`
• 
  `x=44`°

Thus the lower bound restriction of x is 44°

We can now solve for the upper bound of x.

• 
  `3x-42=180`

• 
  `3x=222`

• 
  `x=74`°

Thus the upper bound restriction of x is 74°