Question

How do I find the value of x here?

Answer 1

In isosceles triangles, both base angles are the same, so the top triangle's second base angle is 65 degrees. Also, vertical angles are equals so the second triangle's base angles are 65 degrees as well. Finally, The 4 angles at the bottom (one of which is angle 2) must equal 360 degrees, so using the vertical angle theorem you can form the equation...

-5 + 12x + -5 + 12x + 65 + 65 = 360
combine like terms
120 + 24x = 360
subtract 120 from both sides
24x = 240
divide both sides by 24
x = 10

Hope this helps :)