# Interior angles of a polygon

1. Aug 13, 2016

### Frank212

1. The problem statement, all variables and given/known data

2. Relevant equations
sum interior angles (n-2)*180
angles of a quadrilateral: a+b+c=d = 360

3. The attempt at a solution
What do you do with the exterior angle?
80+130+a+x=360

2. Aug 13, 2016

### Ray Vickson

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

3. Aug 13, 2016

### Frank212

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

4. Aug 13, 2016

### Ray Vickson

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.)
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}