Question

Answer to each question

Answer 1

10. x = 7

11. x = 4

12. x = 6, m<CBD = 38

13. x = 9

Explanation:

(All these problems are solved in practically the same way)

10:

AD and CD are perfect halves of the line AC split by BD, meaning they are the same length. This means you can set up the equation:

`10x+4=6x+32`

Which will then get you
`x=7`

11:

AB and BC are the same length because they are on opposite sides of the isosceles triangle. This means you can set up the equation:

`5x-3=2x+9`

Which will then get you
`x=4`

12:

m<ABC and m<CBD is just the m<ABC split perfectly by line BD. This means you can set up the equation:

`7x-4=3x+20`

Which will then get you
`x=6`

You can then plug in x to the equation
`3x+20` which will get you:

m<CBD = 38

13:

m<A and m<C are opposite angles on the isosceles triangle, meaning they're equal to each other. This means you can set up the equation:

`4x+2=2x+20`

Which will then get you
`x=9`