Question

Could you help with

Answer 1

We have 3 triangles that are related in the image

We will use the sine relations to determine the value of x

For triangle ABD

`\begin{gathered} (24)/(\sin d)=(16)/(\sin b)=(2x+4+2x)/(\sin a) \\ \\ (24)/(\sin d)=(16)/(\sin b)=(4x+4)/(\sin a) \\ \\ \end{gathered}`

For triangle ABC

`(24)/(\sin c1)=(E)/(\sin b)=(2x+4)/(\sin a1)`

For triangle ACD

`(16)/(\sin c2)=(E)/(\sin d)=(2x)/(\sin a2)`

Now solving the system of equations we have

`\begin{gathered} 4x+4=20 \\ 4x=20-4 \\ 4x=6 \\ x=4 \end{gathered}`

The answer would be x = 4 units