Question

Find the value of x in each case. Give reasons to justify your solutions!

B, C ∈ AD

Please help me :)

Answer 1

x = 13

Explanation:

Find the diagram attached

From the diagram, the sum of angle of the straight line BCD is 180°. Hence;

<BCE+<ECF<90 = 180

<BCE+64+90=180

<BCE+154 = 180

<BCE = 180-154

<BCE = 26°

Next is to get x.

The sum of interior angles <BCE and <BEC is equal to exterior angle <ABE

<BCE + <BEC = <ABE

26+x = 3x

Collect like terms

26 =3x-x

26=2x

x = 26/2

x = 13

Hence the value of x is 13

Answer 2

`x=13`

Explanation:

`m\angle ACF=90\degree`

`\therefore \angle BCE=90-64=26\degree`

By the remote exterior angle property,

`m\angle BCE+m\angle BEC=m\angle ABE`

`\implies x+26=3x`

`\implies 3x-x=26`

`\implies 2x=26`

`\implies x=13`