Question

Find x if angle abd =4x-30 and angle cbd=x-6 if line bd bisects angle abc. Find angle abc also

Answer 1

Therefore, x = 8

Explanation:

Given: see the figure

∠ abd = 4x - 30

∠ cbd = x - 6

line bd bisects ∠ abc

i.e ∠ abd = ∠ cbd ........... Definition of Angle bisector.

To Find:

x = ?

Solution:

line bd bisects ∠ abc

i.e ∠ abd = ∠ cbd ........... Definition of Angle bisector.

On substituting the values we get

`4x-30=x-6\\\\4x-x=30-6\\\\3x=24\\\\x=(24)/(3) \\\\x=8`

Therefore, x = 8