Question

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

Answer 1

Answer:

Follows are the solution to this question:

Step-by-step 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:

$\to \frac{6}{x}=\frac{4}{6}\\\\\to 6 \times 6 = 4 \times x\\\\\to \frac{6 \times 6}{4} = x\\\\\to x =\frac{36}{4} \\\\\to x =9$

In point (ii):

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

according to bisector theorem:

$\to \frac{8}{4}=\frac{6-y}{y}\\\\\to \frac{2}{1}=\frac{6-y}{y}\\\\ \to 2 =\frac{6-y}{y}\\\\\to 2y = 6-y\\\\ \to 2y+y 6\\\\ \to 3y =6 \\\\ \to y = \frac{6}{3}\\\\\to y= 2$