Question

Find X, Angle bisector

Answer 1

Since BD is an angle bisector, it cut the angle into two equal angles.

∠ABD = ∠CBD       definition of angle bisector

 3x - 1 = 34 - 2x      substitution

  5x - 1 = 34            added 2x to both sides

   5x    = 35            added 1 to both sides

      x    = 7              divided both sides by 5

Answer: 7

Note: Since it is given that m∠ABC = 40°, we could have calculated the ∠ABD = 20 and created the equation: 20 = 3x - 1.  Once solved, we will get x = 7

Answer 2

x = 7

∠ABD = ∠CBD = 20 ( BD bisects ∠ABC )

solve either 3x - 1 = 20 or 34 - 2x = 20

3x - 1 = 20 ( add 1 to both sides and divide by 3 )

3x = 21 ⇒ x = 7

OR

34 - 2x = 20 ( subtract 34 from both sides and divide by - 2 )

- 2x = - 14 ⇒ x = 7