Question

A b and c lie on a straight line given that angle y = 125 and angle z = 313 work out x

Answer 1

`x=78`

Explanation:

Skills needed: Exterior Angle Theorem, Triangle Geometry:

1) We need to solve for
`x` and there are 2 methods to do it. I will go over the fastest way (since it's better).

• This involves the exterior angle theorem (see the image attached to see how that works.

2) In order to use this theorem, we need to solve for the angle near
`z`. This angle would be
`360-z`, which is
`360-313` (since
`z=313`).

`360-313` =
`47`

3) Then, we can use the fact that
`y=x+47` (47 is the measure of the angle we just solved for.)

`y=125`, so
`125=x+47`

Subtract 47 from both sides, and get
`x=78`

Hope you understood and have a nice day! :D

Note: I have attached one image that shows my work, and another image that shows the exterior angle theorem (which I created on a whiteboard). Hope you get it! If you have any questions, comment and I can answer it ASAP!

Answer 2

∠x = 78

Explanation:

∠y + ∠1 = 180

=> 125 + ∠1 = 180

=> ∠1 = 180 - 125

=> ∠1 = 55

∠z + ∠2 = 360

=> 313 + ∠2 = 360

=> ∠2 = 360-313

=> ∠2 = 47

∠1 + ∠2 + ∠x = 180

=> 55 + 47 + ∠x = 180

=> ∠x = 180 - 55 - 47

=> ∠x = 78