SOLUTION: For concave pentagon ABCDE, find the measure of the reflex angle at vertex E (in degrees) if m∠A = m∠D = x°, m∠B = m∠C = (3x)°, and the measure of the reflex angl

Algebra ->  Length-and-distance -> SOLUTION: For concave pentagon ABCDE, find the measure of the reflex angle at vertex E (in degrees) if m∠A = m∠D = x°, m∠B = m∠C = (3x)°, and the measure of the reflex angl      Log On


   

Question 1191966: For concave pentagon ABCDE, find the measure of the reflex angle at vertex E (in degrees) if
m∠A = m∠D = x°,

m∠B = m∠C = (3x)°,
and the measure of the reflex angle at vertex E is (7x)°.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A concave polygon has at least one "sunk in" place. That means it
has an interior angle which has measure greater than 180o.
It is indicated with the red arc.



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

S%22%22=%22%22%28n-2%29180%5Eo

A pentagon has 5 sides so n=5

S%22%22=%22%22%285-2%29180%5Eo
S%22%22=%22%22%283%29180%5Eo
S%22%22=%22%22540%5Eo

So we add the angle measures and set that equal to 540o.

m∠A + m∠B + m∠C + m∠D + m∠E = m∠D = 540o

xo + (3x)o + (3x)o + xo + (7x)o = 540o 

(15x)o = 540o 

xo = 36o 

You can answer the questions from here.

Edwin