What is the sum of the exterior angles, one at each vertex, of any convex polygon?
for each vertex, sum of exterior angle and interior angle = 360 so for N vertices, that sum is N*360 for any conves polygon, sum of all interior vertices = (N-2)*180 thus sum of all exterior angles = N*360 - (N-2)*180 = N*180 + 360
Geometry question ( measures of angles )?
there are to possible answers to your question: if we talk about the basis vertex or basis angle if you would like to call it that way. we should call the interner angel x and the exterior angle 3x (as given forementioned). in straight line the sum of angles is 180, so in that case: 3x+x=4x=180 x=45(exterior angle+interior angle are always equal 180) so the angels of the triangle will be 45,45,90(against equal sides there are equal angles and in triangle the sum of angle is 180). in the other case that i have mentiond before, the head angle equals x and the exterior to it equals 3x so the head angle equals 45 and the other angles equals 67.5(because of the same reasons as before). hope that i have helped yoav zilberman
Geometry Question about Exterior Angles?
Okay so I'm not sure if it's a typo on my study guide or if I'm just doing it wrong, but the measurement I got for an angle was -5 degrees and I really doubt that's a possible answer. The problem is triangle TRI and it's exterior angle. The measurement of the exterior angle is 7a+50 and the two remote interior angles are 2a+80 and 70-3a. It want's to know the measurement of
Thanks for the A2A.Since, the ratio of its internal to external angle is 7:2, you can say that its internal angle = 7x and exterior angle = 2x.Therefore, 7x + 2x = 180=> x = 20Exterior angle = 40 degreesnow (exterior angle) = 360/(no. of sides)solving, you will get no. of sides = 9.
State the sum of the measures of the exterior angles(one at each vertex) of a polygon with 7 sides?
Sum of the measures of all exterior angles of any n sided polygon is always 360 degrees. Hence here also it is only 360 degrees.
Geometry questions?!!?
Hi, The exterior angles of any convex polygon with one at each vertex always add to 360°. An interior and exterior angle always add to 180°. Find the number of sides of a regular polygon if one interior angle is 60 degrees. If the interior angle is 60°, then the exterior angle is 180 - 60 or 120°. Since all the exterior angles add to 360, then 360/120 = 3. This "regular polygon" is an equilateral triangle. For the second part, you didn't give a number, so I will give you several examples. One exterior angle of a regular pentagon measures 45°. How many sides are there? 360/45 = 8 so it has 8 sides and is an octagon. One exterior angle of a regular pentagon measures 72°. How many sides are there? 360/72 = 5 so it has 5 sides and is a pentagon. One exterior angle of a regular pentagon measures 36°. How many sides are there? 360/36 = 10 so it has 10 sides and is a decagon. One exterior angle of a regular pentagon measures 15°. How many sides are there? 360/15 = 24 so it has 24 sides and is a 24-gon. I hope that helps!! :-)
Geometry Question. Please Help?
Q1. Let x be base angle & y be vertex angle, So, 2x+y = 180 (Sum of angles in isosceles triangle) x+7 = 4y (From given info.) Then, solve the simultaneous equations, and hence, x & y values can be found. Q2. (180 - 52) / 2 = 64 (Sum of angles in isosceles triangle) 64/2 = 32 (Angle bisector) 32+52 = 84 (2 interior angles = 1 exterior angle) Hence, answer: 84 Q3. 180 - 130 = 50 (Angles on a straight line) So, Base angle = 50 180 - 50 - 50 = 80 (Sum of angles in isosceles triangle) So, Vertex angle = 80 Hence, answer: 50, 50, 80 Q4. Each angle in equilateral triangle = 180/3 = 60 60/2 = 30 (Angle bisector) 180 - 30 - 30 = 120 (Sum of angles in the obtuse-angled triangle) Hence, answer: 120
First, Let’s sum up what we should know to solve this problemThere’s this property of closed polygons that the sum of all the exterior angles is [math]360°[/math]The sum of an interior angle with it’s respective exterior angle is [math]180°[/math]And, it is obvious that the number of exterior angles is equal to the number of sidesA triangle has 3 exterior anglesA square has 4A decagon has 10 (and so on.)In a regular polygon all the exterior angles are equal .(As internal angles are equal. To prove use 2. )Let’s StartFinding the exterior angleWe assume the exterior angle to be [math]x.[/math]So According to the question, the interior angle must be [math]108° + x[/math]By using 2. we get[math]108° + x + x = 180°[/math]On solving for x, we will get[math]x=36°[/math]Finding the number of sidesNow from 1. and 3., we can conclude thatExterior Angle* Number of sides(n)[math]=360°[/math][math]=> 36° * n =360°[/math][math]=> n= 360°/36° = 10[/math]Thus, there are 10 sides in the regular polygon.
Can a triangle have 6 exterior angles?
Yes, it depends on which side of triangle you extend past vertex Here's an example that shows triangle with exterior angles drawn two different ways. In each instance there are only 3 exterior angles, but taking both together, we get 6 exterior angles: http://www.flickr.com/photos/56185495@N0... Note that since interior angle + exterior angle = 180 at each vertex, then α₁ = α₂ β₁ = β₂ θ₁ = θ₂ Also note that in any polygon, sum of exterior angles = 360. Therefore: α₁ + β₁ + θ₁ = 360 α₂ + β₂ + θ₂ = 360 Now if triangle ABC is equilateral, then α₁ = β₁ = θ₁ = 360/3 = 120 α₂ = β₂ = θ₂ = 360/3 = 120 All six exterior angles of a triangle may be obtuse. -----> TRUE Ματπmφm
This is a very interesting as well as a very confusing question. One who knows the basics of Geometry can solve this type of questions very easily. You too can able to solve this type of problems when you come to know the basics of Geometry.There is a simple rule that the sum of all interior angles of a Triangle always 180*. In any condition if an area covered with three sides whether the length of the sides. All three side may be of same length or two sides of the triangle be same length and the third side is of different than the other two sides the some of all interior angles always be of 180*.There is a theorem to prove that the sum of all three angles always be of 180*. So it’s simple a closed area with three or more straight lines we get separate the shape into triangles. Because,A triangle (3 Sides) = 1*180 = 180 (the sum of all interior angles of a triangle)Hence,A quadrilateral (4 Sides) = 2 * 180 = 360*(there are 2 triangle in quadrilateral)A pentagon (5 Sides) = 3 * 180 = 540 (there are 3 triangles in a pentagon)Hexagon (6 Sides) = 4 * 180 = 720 (there are 4 triangles in a hexagon)Heptagon (7 Sides) = 5 * 180 = 900* (there are 5 triangles in a heptagon)…….So,A polygon (n sides) = (n-2) * 180.Examples: If a polygon having 15 sides, the sum of all interior angles would be-13 * 180 = 2340.