SOLUTION: Determine the measure of the interior angle at vertex A. It is a pentagon, at vertex A is 3x This is how it is set up 4x

Algebra ->  Polygons -> SOLUTION: Determine the measure of the interior angle at vertex A. It is a pentagon, at vertex A is 3x This is how it is set up 4x       Log On


   

Question 202530: Determine the measure of the interior angle at vertex A.
It is a pentagon, at vertex A is 3x This is how it is set up
4x
4x 4x
3x 3x vertex A
Answers
A. 150 B. 50 C.90 D.30
The answer is 90 but can't figure out how they got it.
Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can start with the formula for the sum (S) of the interior angles of a polygon with n sides:
S+=+%28n-2%29%2A180 In this problem, you have a pentagon so n =5.
The sum of the interior angles can be expressed as:
S+=+4x%2B4x%2B4x%2B3x%2B3x Add up the x's.
S+=+18x Now set this equal to %28n-2%29%2A180 where n = 5 (for pentagon).
%285-2%29%2A180+=+18x
3%2A180+=+18x Divide both sides by 18.
3%2A10+=+x so that...
x+=+30
The angle at vertex A is 3*x, so...
3x+=+3%2A30=90
highlight%28A+=+90%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the interior angles of any polygon is degrees where is the number of sides (or vertices, if you will) of the polygon. You have a pentagon so , hence the sum of the interior angles is

Your angles are given as , , , , and , so:



Just solve for and then multiply by 3 to get the measure of angle A, or by 4 to get the measure of any one of the larger angles.


John