Question
All sides of a regular pentagon are extended to form a star with vertices P,Q,R,S,T. What is the sum of the angles made at the vertices?___
Answer:
:
Interior angle = [(2n-4)x90]/n = 108
2x= 360-(108x2) = 144
angle P = 180-144= 36
Total = 36x5= 180
Useful to remember: Sum of angles in a star= 180∘
Shortcut: Clearly the star point trisects the angle in a pentagon. Hence each angle = 108/3 = 36.
Sum of angles = 36*5 = 180
Alternatively: Sum of angles of a n point star = (n – 4) x 180∘, where n = number of sides of a polygon.
Here, n = 5.Sum of angles of a n point star = (5 – 4) x 180∘=180∘.
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:
Interior angle = [(2n-4)x90]/n = 108
2x= 360-(108x2) = 144
angle P = 180-144= 36
Total = 36x5= 180
Useful to remember: Sum of angles in a star= 180∘
Shortcut: Clearly the star point trisects the angle in a pentagon. Hence each angle = 108/3 = 36.
Sum of angles = 36*5 = 180
Alternatively: Sum of angles of a n point star = (n – 4) x 180∘, where n = number of sides of a polygon.
Here, n = 5.Sum of angles of a n point star = (5 – 4) x 180∘=180∘.
Was this answer helpful ?
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