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Thiru · Answer 1 · 2023-10-23T20:58:12+0000

SOLUTION

Notice that the angles formed at the center are all equal

Hence,

$\begin{gathered} m\angle1=(360^(\circ))/(8) \\ m\angle1=45^(\circ) \end{gathered}$

Notice that:

$m\angle2=(m\angle1)/(2)$

Hence it follows:

$\begin{gathered} m\angle2=(45^(\circ))/(2) \\ m\angle2=22.5^(\circ) \end{gathered}$

Note that the value of each angle of the octagon is:

$\begin{gathered} (180^(\circ)(8-2))/(8) \\ =135^(\circ) \end{gathered}$

Hence it follows:

$\begin{gathered} m\angle3=(135^(\circ))/(2) \\ m\angle3=67.5^(\circ) \end{gathered}$

Therefore the answers are:

$m\operatorname{\angle}1=45^{\operatorname{\circ}},m\operatorname{\angle}2=22.5^{\operatorname{\circ}},m\operatorname{\angle}3=67.5^{\operatorname{\circ}}$

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