In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of: (i) ∠AOB, (ii) ∠ACB,

Home » In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of: (i) ∠AOB, (ii) ∠ACB,

In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of: (i) ∠AOB, (ii) ∠ACB,

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(B) - 7

Solution:

(i)

$Arc\text{ }AB$

subtends

$\angle AOB$

at the centre and

$\angle ACB$

at the remaining part of the circle.

$\angle ACB\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\angle AOB$

And as

$AB$

is the side of a regular hexagon,

$\angle AOB\text{ }=\text{ }{{60}^{o}}$

(ii) Now,

$\angle ACB\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }({{60}^{o}})\text{ }=\text{ }{{30}^{o}}$

i

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