We can solve the problem in the following manner.
Given to us
∠CAB = 60°
1. What is m∠ACB?
Given,
∠CAB = 60°
ΔACB
CA= CB = radius of the circle,
therefore,
∠CAB = ∠CBA = 60°
sum of all the angles of a triangle
the sum of all the angles of a triangle is 180°
so, ∠CAB + ∠CBA + ∠ACB = 180°
60° + 60° + ∠ACB = 180°
120° + ∠ACB = 180°
∠ACB = 180° - 120°
∠ACB = 60°
Hence, the value of ∠ACB is 60°.
2. What is the length of segment AB?
As in ΔACB, all the angles are equal. thus, the triangle is an equilateral triangle.
For an equilateral triangle, all the sides of the triangle are equal.
AB = BC =CA = radius of the triangle.
Hence, the length of the segment AB is the radius of the circle.
3. What is the perimeter of the hexagon?
The perimeter of the hexagon is given as 6a, where a is the side of the hexagon.
perimeter of the hexagon = 6 x a
perimeter of the hexagon = 6 x side(AB)
perimeter of the hexagon = 6r
Hence, the perimeter of the hexagon is 6r.
4. The perimeter of the hexagon is ___ the circumference of the circle.
perimeter of the hexagon = 6r
perimeter of the circle = 2 π (radius)
[tex]=2\times\pi\times r\\=2\times 3.14 \times r\\=6.28\ r[/tex]
Hence, the perimeter of the hexagon is less than the circumference of the circle.
5. The circumference of the circle is ___.
perimeter of the circle = 2 π (radius)
[tex]=2\times\pi\times r\\=2\times 3.14 \times r\\=6.28\ r[/tex]
Hence, the circumference of the circle is slightly greater than 6.
Learn more about Regular hexagons:
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