An interior angle of a dodecagon is 150 degrees. An interior angle of an octagon is 135 degrees. So the angles of 2 dodecagons and 1 octagon would sum to 435 degrees. A point in the plane has 360 degrees around it. Angles that sum to 435 degrees would, therefore, result in overlap.
You say these things to yourself: -- "The perimeter is the distance all the way around the octagon." -- "The octagon has eight sides." -- "So, if it's a 'regular' octagon, then all the sides are the same length, and each side must be 1/8 of the perimeter." -- If it's not a 'regular' octagon, then it has some longer sides and some shorter ones, and the perimeter doesn't help me find the lengths of the sides.
It is a regular 8 sided octagon
He will have skated a full turn of 360 degrees
They add to 360 degrees.
360 degrees
A) 68 degrees B) 135 degrees C) 90 degrees D) 45 degrees
An interior angle of a dodecagon is 150 degrees. An interior angle of an octagon is 135 degrees. So the angles of 2 dodecagons and 1 octagon would sum to 435 degrees. A point in the plane has 360 degrees around it. Angles that sum to 435 degrees would, therefore, result in overlap.
To be able to tessellate where a vertex meets other vertices, the total of those angles must be a full circle of 360°. The interior angle of an Octagon is 135° which does not divide into 360° which means there cannot be a complete number of vertices meeting and so it cannot, by itself, tessellate. However, two octagons meeting at a point would have 135° + 135° = 270° leaving 90° which is the interior angle of a square. So octagons and squares together will tessellate.
The angles of a n-sided regular polygon have the measure of (n-2)*180/n degrees. A regular octagon's angle has (8-2)*180/8 = 6*180/8 = 135 degrees. If you stick together two sides of two different (but congruent) regular octagons you get one downward and one upward. We can say this without loss of generality because up and down are just perspective that you can change as you look around the construction. So, at the left of the common side you have two angles around the vertexes. Both of the angles have 135 degrees (being angles of regular octagons). But there is a third angle. The sum of the measures of angles around a point is 360 degrees. So the third angle has 360-135-135 = 90 degrees. And the two sides that form the angle are congruent. ==> you construct a square.
You say these things to yourself: -- "The perimeter is the distance all the way around the octagon." -- "The octagon has eight sides." -- "So, if it's a 'regular' octagon, then all the sides are the same length, and each side must be 1/8 of the perimeter." -- If it's not a 'regular' octagon, then it has some longer sides and some shorter ones, and the perimeter doesn't help me find the lengths of the sides.
An octagon does not have 180 degrees. Consider, - travelling anti clockwise around the Octagon, we first turn 45o to the SW, followed by another turn of 45o to the S. And so around the octagon till we have turned left eight times. A total of 360 degrees. (Almost by definition since we finish up where we started.) That is the sum of the external projected angles - the deflections from a straight line. The internal angles are 135o , (180 - 45), so the sum of the internal angles is 8 x 135.
It is a regular 8 sided octagon
Regular ice water is typically around 0 degrees Celsius (32 degrees Fahrenheit).
1080 Consider an octagon. Now draw a line along one side, and extend it a little beyond the angle where it turns to the next side.If you think this through, you'll see that if you repeated this exercise 8 times around the octagon, you'd now be alongside the first line. In other words, you have turned 360 degrees.So 360o for 8 turns, = 360/8 = 45o for each turn. That angle is the angle turned through. Therefore the internal angle is 180o - 45o = 135o.The same experiment for pentagon, regular triangle and so on.The 8 interior angles of an octagon add up to 1080 degrees.
He will have skated a full turn of 360 degrees
He will turn 720 degrees because the angle sum of a hexagon is 720 degrees