Question

Given the regular octagon, what is the measure of each numbered angle? (image attached)thank you ! :)

Answer 1

SOLUTION

Notice that the angles formed at the center are all equal

Hence,

$\begin{gathered} m\angle1=\frac{360^{\circ}}{8} \\ m\angle1=45^{\circ} \end{gathered}$

Notice that:

$m\angle2=\frac{m\angle1}{2}$

Hence it follows:

$\begin{gathered} m\angle2=\frac{45^{\circ}}{2} \\ m\angle2=22.5^{\circ} \end{gathered}$

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

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

Hence it follows:

$\begin{gathered} m\angle3=\frac{135^{\circ}}{2} \\ m\angle3=67.5^{\circ} \end{gathered}$

Therefore the answers are:

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