Each interior angle of a regular polygon has a measure of 162. How many sides does the polygon have ?
the front sail of a sailboat is a triangular cloth 40 feet high and 30 feet long. What is the perimeter of the front sail?
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#2) If each interior angle has a measure of 162º, then each exterior angle has a measure of 180-162=18º.
How many angles are there ? The sum of the measures of the exterior angles of a convex polygon of n sides is 360º. 360/18=20 angles and therefore 20 sides.
check:There are 20 angles of 162º each for a total of 162*20=3240º
To find the sum of all the interior angles of a regular polygon you use the formula (n-2)180 where n=# of sides.
If we assume that the triangle is a right triangle then
we would have the two legs of the triangle and we could find the third side
Using the pythagorean thereom
C2 = a2 + b2 , where a = 30 and b=40
then a2 + b2 = 900 + 1600
C2 = 2500
c = 50
Perimeter = 30 + 40 +50 = 120
If it is isosceles you could find the lenght of the two equal sides and then find the perimeter
Otherwise, you would need an angle and then use the law of sines to find the third side