The measure of arc ABC is 120r, arc ACE is 240r, arc AB is 60r and angle is 60⁰.
What is a hexagon inscribed in a circle?
A regular hexagon is a polygon whose all sides are equal and it is made of six equilateral triangle.
If a hexagon inscribed in a circle then its side is equal to the radius of circle.
Now, suppose 'r' is the radius of circle.
and if opposite sides of the hexagon ABCDEF are joined dividing the hexagon in 6 equal parts, it forms six angles at centre.
⇒Angles at centre of each triangle = 360/6 = 60⁰.
Now, Since angle =arc/radius
and angle of each triangle is 60⁰
Therefore, 60 = arc/r
⇒ arc = 60r
⇒ arc AB = arc BC = arc CD = arc DE = arc EF = 60r
Hence,
arc ABC = arc AB + arc BC
⇒ arc ABC = 60r + 60r = 120r
∴ arc ACE = arc AB + arc BC + arc CD + arc DE
⇒arc ACE = 60r + 60r + 60r + 60r
⇒ arc ACE = 120r + 120r = 240r
Hence,the measure of arc ABC is 120r, arc ACE is 240r, arc AB is 60r and angle is 60⁰.
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