Question 1191966
<pre>
A concave polygon has at least one "sunk in" place. That means it
has an interior angle which has measure greater than 180<sup>o</sup>.
It is indicated with the red arc.

{{{drawing(400,400,-.2,2,-.2,2,

locate(0,0,A), locate(1.6,0,B),locate(1.83,.63,C),locate(.48,1.63,D),
locate(.72,.65,E),

red(arc(.809,.588,.5,-.5,216,468)),

locate(.2,.16,x^o),locate(1.42,.16,(3x)^o),locate(1.57,.62,(3x)^o),
locate(.84,.7,(7x)^o),locate(.6,1.4,x^o),

line(0,0,1.618,0), line(1.618,0,1.809,.588), line(1.809,.588,.5,1.549),
line(.5,1.549,.809,.588), line(.809,.588,0,0) )}}}

The sum of all measures of an n-sided polygon is given by
the formula:

{{{S}}}{{{""=""}}}{{{(n-2)180^o}}}

A pentagon has 5 sides so n=5

{{{S}}}{{{""=""}}}{{{(5-2)180^o}}}
{{{S}}}{{{""=""}}}{{{(3)180^o}}}
{{{S}}}{{{""=""}}}{{{540^o}}}

So we add the angle measures and set that equal to 540<sup>o</sup>.

m∠A + m∠B + m∠C + m∠D + m∠E = m∠D = 540<sup>o</sup>

x<sup>o</sup> + (3x)<sup>o</sup> + (3x)<sup>o</sup> + x<sup>o</sup> + (7x)<sup>o</sup> = 540<sup>o</sup> 

(15x)<sup>o</sup> = 540<sup>o</sup> 

x<sup>o</sup> = 36<sup>o</sup> 

You can answer the questions from here.

Edwin</pre>