MHB Sum of the measures of the interior angles of a heptagon

AI Thread Summary
The sum of the interior angles of a heptagon is 1260°, calculated using the formula (n-2)180°, where n is the number of sides. For a polygon with a sum of interior angle measures of 3600°, it has 22 sides, derived from rearranging the same formula. Each exterior angle of a regular octagon measures 45°, as the sum of exterior angles for any polygon is always 360°. The discussion emphasizes the importance of understanding these formulas for solving polygon angle problems. Accurate calculations are essential for determining angle measures in various polygon types.
yormmanz
Messages
2
Reaction score
0
PLEASE HELP1.What is the sum of the measures of the interior angles of a heptagon?

A. 1260∘
B. 2520∘
C. 900∘
D. 1800∘

my answer is C

5.If the sum of the interior angle measures of a polygon is 3600∘, how many sides does the polygon have?
A. 22 sides
B. 20 sides
C. 18 sides
D. 10 sides

MY ANSWER ?

3.What is the angle measure of each exterior angle of a regular octagon?
A. 45∘
B. 135∘
C. 360∘
D. 1080∘

MY ANSWER ?
 
Mathematics news on Phys.org
couple of pieces of information to assist you ...

the sum of the interior angles of a convex n-gon is $(n-2)180^\circ$

the sum of the exterior angles of a convex n-gon is $360^\circ$
 
Last edited by a moderator:

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB Finding the Measure of Angle KPM Using Angle Bisector Theorem
Replies
2
Views
1K
MHB What is the measure of angle KPM?
Replies
5
Views
1K
MHB Edgar's Question from Facebook: Convex Polygon
Replies
1
Views
3K
MHB Act.ge.5 third angle of triangle
Replies
1
Views
1K
Interior and Exterior Angle of a Polygon: Formula not working
Replies
3
Views
2K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
Replies
2
Views
1K
MHB Internal angle sum of triangle
Replies
1
Views
2K
Sum of a polygon's interior angles
Replies
39
Views
22K
I Dimension of an Angle: Clarifying the SI Standard
Replies
1
Views
2K
MHB Find unknown angles of a triangle
Replies
6
Views
3K

Hot Threads

Recent Insights

Back
Top