Question

Find the value of each variable. Simplify your answer as much as possible.

Answer 1

Follows are the solution to this question:

Explanation:

In the given question an attached file is missing, which can be defined as follows please find it.

In part (i):

In the
`\triangle ABC`, the side BD bisector of
`\angle B`:

according to bisector theorem:

`\to (6)/(x)=(4)/(6)\\\\\to 6 * 6 = 4 * x\\\\\to (6 * 6)/(4) = x\\\\\to x =(36)/(4) \\\\\to x =9 \\\\`

In point (ii):

In the
`\triangle ADB`, the side BD bisector of
`\angle A`:

according to bisector theorem:

`\to (8)/(4)=(6-y)/(y)\\\\\to (2)/(1)=(6-y)/(y)\\\\ \to 2 =(6-y)/(y)\\\\\to 2y = 6-y\\\\ \to 2y+y 6\\\\ \to 3y =6 \\\\ \to y = (6)/(3)\\\\\to y= 2`