Question

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

Answer 1

Answer:

$x=78$

Step-by-step 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

Answer:

∠x = 78

Step-by-step 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