Simplifying Exterior Angles in a Polygon

[Frank212]

Homework Statement

Homework Equations

sum interior angles (n-2)*180
angles of a quadrilateral: a+b+c=d = 360
[/B]

The Attempt at a Solution

What do you do with the exterior angle?
80+130+a+x=360

 

[Ray Vickson]

Homework Statement

View attachment 104635

Homework Equations

sum interior angles (n-2)*180
angles of a quadrilateral: a+b+c=d = 360
[/B]

The Attempt at a Solution

What do you do with the exterior angle?
105+80+130+a+x=360

How would you find $x$ from the information in the diagram?

 

[Frank212]

How would you find $x$ from the information in the diagram?

a+130+x=360
180-100=80
x=80
130+80+85= 295
360-295=65
a=65

 

[Ray Vickson]

a+130+x=360
180-100=80
x=80
130+80+85= 295
360-295=65
a=65

Much easier: just use the fact that 100+x = 180, because the angles 100 and x make up a straight line. (I know you got the correct value for x above, but I found your argument to be confusing and not as step-by-logical-step as it should be.)