Question

Find X, Angle bisector

Answer 1

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

Answer 2

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