Can you solve these, and explain how you got the answers too?Thanks!
1. How many distinct diagonals does a hexagon have?
2. How many sides would a regular polygon have if each interior angle measures 162°?
3. How many angles would a regular polygon have if each exterior angle measures 5°?
2006-08-18 05:31:48 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
thanks pablo fanques! you get 10 points!
2006-08-18 05:44:40 · update #1
1. If a polygon has N sides then the number of diagonals is given
by the following expression:
(N *(N - 3))/2
A hexagon has 9 distinct diagonals.
You can find an explanation of the formula here
http://mathforum.org/library/drmath/sets/select/dm_polygon_diagonals.html
2. ((N-2) * 180) / N = 162°
Solve for N
(162°)N = (180°)N - 360°
(-18°)N = -360°
N = 20
3. Interior angle = 180° - Exterior angle
Interior angle = 175°
(175°)N = (180°)N - 360°
(-5°)N = - 360°
N = 72
2006-08-18 05:36:25 · answer #1 · answered by Pablo Fanques 3 · 0⤊ 1⤋
2 & 3. Draw a line out from the angle and measure its supplement to find the exterior angle. For 162°, it's 18°. The 5° is already an exterior angle. The sum of the exterior angles must be 360°. If it's a regular polygon, divide 360° by the exterior angle, and you'll know how many you have. (20 and 72.)
2006-08-18 12:46:19 · answer #2 · answered by TychaBrahe 7 · 0⤊ 0⤋
6 12 75
2006-08-18 12:37:13 · answer #3 · answered by The::Mega 5 · 0⤊ 0⤋
3
20
72
yeah of course 3 20 and 72
2006-08-18 12:38:13 · answer #4 · answered by Anonymous · 0⤊ 0⤋
i dont really know but stop using yahoo answers 4 ur hmwk cuz some ppl will give u the wrong answers.
2006-08-18 12:37:24 · answer #5 · answered by jjimenez93 1 · 1⤊ 0⤋
1.)
6C2 = (6!)/(2!(6 - 2)!)
6C2 = (6!)/(2!(4!)
6C2 = (6!)/48
6C2 = 15
ANS : 15
2.)
beta = (180(n - 2))/n
162 = (180(n - 2))/n
162n = 180(n - 2)
162n = 180n - 360
-18n = -360
n = 20
ANS : 20
----------------------------------
3.)
alpha = 360/n
alpha = 360/5
alpha = 72
ANS : 72
2006-08-18 15:27:15 · answer #6 · answered by Sherman81 6 · 0⤊ 0⤋
1. one
2. 20
3. at least do this one yourself
2006-08-18 12:45:13 · answer #7 · answered by Arkham 1 · 0⤊ 0⤋
oo shits i remeber this but i don't know how to answer this becuz when my teacher was teachin this stuff i fell asleep
2006-08-18 12:37:38 · answer #8 · answered by Anonymous · 0⤊ 0⤋
I don't know... So much for this college education!
2006-08-18 12:38:42 · answer #9 · answered by J-Rod 2 · 0⤊ 0⤋
hold on let me get my geometry book
brb this is so easy basic stuff
MR TICKED OFF IS WAY OFF
2006-08-18 12:36:52 · answer #10 · answered by Anonymous · 1⤊ 1⤋