The sum of the interior angles of an n gon is <span> (n-2)*180
the measure of each interior angle is </span><span>(n-2)*180/n
the measure of each individual exterior angle of an ngon is 360/n
all exterior angles add to 360
1. sum of 15 gon is
(15-2)*180=13*180=2340 degrees
2. deca is 10
(10-2)*180/10=8*18=144 degrees
3. dodecagon is 12 sides
360/12=30 degrees
4. 4 sides, those are exterior angles, so they add to 360
4r+7r+8r+5r=360
24r=360
r=15 degrees
5.
pentagon or 5 sides
sum of internal is (5-2)*180=3*180=540 degrees
540=4z+5z+3z+5z+3z
540=20z
27 degrees=z
3z=81=A=D
4z=108=B
5z=135=C=E
6. (n-2)*180
20 gon
(20-2)*180=18*180=3240 degrees
7. exterior angles add to 360
4y+2y+4y+6y=360
16y=360
y=22.5
2y=45 degrees
4y=90 degrees
6y=135 degrees
8. interior angles of 4 gon sum is
(4-2)*180=2*180=360
2n+6n+5n+2n=360
15n=360
n=24
2n=48
5n=120
6n=144
9.
6gon
(6-2)*180=4*180=720
90+90+x+x+22+x+x+22=720
224+4x=720
minus 224 both sides
4x=496
divide by 4
x=124
10., exterior angle of pentagon, 5 gon
360/5=72=x
11.
(n-2)*180/n=4*(360/n)
times both sides by n
(n-2)*180=4*360
divide both sides by 180
n-2=4*2
n-2=8
n=10
10 sides
12.
area of octogon of side is
</span>2(1+√2)s² where s is the side length
given, 12=side length
A=2(1+√2)12²
A=2(1+√2)144²
A=288(1+√2)
A=288+288√2 square cm
Let x be the number of child admission tickets sold:
Child's ticket = x
There is a total of 145 tickets sold:
Adult = 145 - x
Total sales is $1020.80:
5.6x + 9.2(145 - x) = 1020.8
Solve for x:
5.6x + 9.2(145 - x) = 1020.8
5.6x + 1334 - 9.2x = 1020.8
3.6x = 313.2
x = 313.2 ÷ 3.6
x= 87
Answer: Number of child's ticket = 87
