Exterior angles of a polygon step 1:Consider, for instance, the ir regular pentagon below.
You need to know four things.Each exterior angle of a regular hexagon = 60°.An exterior angle is the angle between a side of a geometrical figure and an adjacent side that is extended outwards.
Exterior angles of a polygon have several unique properties.The height of the triangle is the apothem of the polygon.
Thus, 70° + 60° + 65° + 40° + x = 360°.The polygon exterior angle sum theorem states that the sum of all exterior angles of a convex polygon is equal to 360º.We can learn a lot about regular polygons by breaking them into triangles like this:
Each exterior angle in a regular pentagon measures 72°.The exterior angles of a polygon add up to 360°.
If there are 9 sides in the polygon, then each exterior angle in the polygon is equal to 360°/9, which is 40°.The formula to determine the sum of exterior angles is derived below:The latter is a circle that passes through all the vertices.
Using linear pair angles are supplementary.For example, for a pentagon, we have to divide 360° by 5:
The sum of the interior angles of a heptagon (7.Sum of exterior angles of polygon = 360º the formula for the exterior angle of a regular polygon with n number of sides can be given as,The sum of the exterior angles in any polygon always add up to 360°.
This question cannot be answered because the shape is not a regular polygon.Substitute n = 6 here:
Last update images today Polygon Exterior Angles Formula
Transfer Talk: Man United Open To Rashford Exit
The 2023-24 season is over with the battles for the major honours, European qualification, relegation and promotion settled.
Here's a roundup of what was decided, and what's still at stake, in the English Premier League, German Bundesliga, Spanish LaLiga, Italian Serie A and French Ligue 1.
- Stream on ESPN+: LaLiga, Bundesliga, more (U.S.)
Premier League Season completed TitleManchester City were crowned champions for a record-setting fourth consecutive season.
Champions League (4)CONFIRMED
1. Man City (38 games, 91 points) 2. Arsenal (38, 89) 3. Liverpool (38, 82) 4. Aston Villa (38, 68) Europa League (2)Man United beat 2-0 Man City in the FA Cup final (stream a replay on ESPN+, U.S. only) to seal one spot in the Europa League (UEL). The second went to fifth place.
CONFIRMED
FA Cup: Manchester United 5. Tottenham Hotspur (38, 66) Europa Conference League (1)CONFIRMED
6. Chelsea (38, 63) Relegation (3)RELEGATED
18. Luton Town (38, 26) 19. Burnley (38, 24) 20. Sheffield United (38, 16)Leicester City and Ipswich Town have been automatically promoted to the Premier League. Southampton beat Leeds United 1-0 in the Championship playoff final (stream a replay on ESPN+, U.S. only) to take the final spot.
LaLiga Season completed Title Real Madrid have been crowned champions.- Stream all LaLiga games live on ESPN+ (US only)
Champions League (4)CONFIRMED
1. Real Madrid (38, 95) 2. Barcelona (38, 85) 3. Girona (38, 81) 4. Atlético Madrid (38, 76) Europa League (2)Athletic won the Copa del Rey and will be in the Europa League, though they will also finish in the first Europa League place in fifth. That means the other UEL place goes to sixth, which Real Sociedad have claimed.
CONFIRMED
5. Athletic Club (38, 68) 6. Real Sociedad (38, 60) Europa Conference League (1)Real Betis cannot be overtaken for the final European place.
CONFIRMED
7. Real Betis (38, 57) Relegation (3)CONFIRMED
18. Cádiz (38, 33) 19. Almería (38, 21) 20. Granada (38, 21)Leganes and Real Valladolid have been promoted into the top flight. Espanyol won the promotion playoffs.
Bundesliga Season completed Title Bayer Leverkusen won the first championship in their history with a remarkable unbeaten record.- Stream all Bundesliga games live on ESPN+ (US only)
Champions League (5)The Bundesliga has sealed an extra place through the European Performance Spot, which sends the team in fifth to the UCL too.
CONFIRMED
1. Bayer Leverkusen (34, 90) 2. VfB Stuttgart (34, 73) 3. Bayern Munich (34, 72) 4. RB Leipzig (34, 65) 5. Borussia Dortmund (34, 63) Europa League (2)Leverkusen beat second division side Kaiserslautern 1-0 in the final of the DFB Pokal (stream a replay on ESPN+, U.S. only), so both sixth and seventh get a UEL place.
CONFIRMED
6. Eintracht Frankfurt (34, 47) 7. TSG Hoffenheim (34, 46) Europa Conference League (1)CONFIRMED
8. Heidenheim (34, 42) Relegation (2+1)Two teams are relegated automatically, while third-bottom takes on third place in the 2. Bundesliga in a playoff.
RELEGATION PLAYOFF
16. VfL Bochum (34, 33)Bochum looked destined to be relegated after losing 3-0 at home to Fortuna Düsseldorf in the first leg ... only for Bochum to win the return leg 3-0 and then secure their top-flight status with a 6-5 penalty-shootout win.
RELEGATED
17. FC Cologne (34, 27) 18. SV Darmstadt 98 (34, 17)St. Pauli and Holstein Kiel have been automatically promoted into the Bundesliga.
Serie A Season completed Title Internazionale wrapped up the Scudetto as runaway champions. Champions League (5) Like Germany, Italy has secured an extra place in next year's competition through its clubs' performance in Europe this season, meaning five clubs have qualified.CONFIRMED
1. Internazionale (38, 94) 2. AC Milan (38, 75) 3. Juventus (38, 71) 4. Atalanta (38, 69) 5. Bologna (38, 68)As Atalanta will finish in the top 4, Italy will remain on five places in the Champions League. Had Atalanta finished fifth, then AS Roma in sixth would also have been in the Champions League next season.
Europa League (2)Juventus won the Coppa Italia, so sixth and seventh will qualify for the UEL.
CONFIRMED
6. AS Roma (38, 63) 7. Lazio (38, 61) Europa Conference League (1)CONFIRMED
8. Fiorentina (38, 60) Relegation (3)RELEGATED
18. Frosinone (38, 35) 19. Sassuolo (38, 30) 20. Salernitana (38, 17)Frosinone began the final day in 16th, but they lost to 17th-placed Udinese, and 18-th placed Empoli scored in the 93rd minute to climb out of the drop zone.
Parma and Cesc Fàbregas' Como were promoted to Serie A automatically, while Venezia beat Cremonese in the playoff final.
Ligue 1 Season completed Title Paris Saint-Germain secured the title with ease. Champions League (3+1)France gets three automatic places, with fourth place entering the UCL in the third qualifying round.
Remarkably Brest were in fourth when the games on the final day entered the 90th minute. Brest scored to go level with Lille on points and goal difference, but Lille stayed third on head to head. Then Lille conceded at home in the fourth minute of added time, sending Brest directly into the Champions League group stage.
CONFIRMED
1. Paris Saint-Germain (34, 76) 2. AS Monaco (34, 67) 3. Brest (34, 61) 4. Lille (34, 59) Europa League (2)The UEL places go to fifth and the winners of the Coupe de France -- PSG beat Lyon 2-1 in the final, so the places passes to sixth ... which is Lyon.
CONFIRMED
5. Nice (34, 55) 6. Lyon (34, 53) Europa Conference League (1)CONFIRMED
7. Lens (34, 51) Relegation (2+1)Two teams are relegated, with third-bottom facing a playoff with a team from the second division to remain in Ligue 1.
RELEGATION PLAYOFF
16. Metz (34, 29)Metz are relegated after they lost 4-3 on aggregate to Saint-Étienne.
RELEGATED
17. Lorient (34, 29) 18. Clermont Foot (34, 25)AJ Auxerre and Angers were automatically promoted to Ligue 1.
