Question

Each angle of a regular octagon has a measure of _____ degrees.

Answer 1

Answer:

The measure of the interior angle of a regular octagon is 135°

Step-by-step explanation:

We have to tell the measure of each angle of a regular octagon.

As octagon has 8 sides and 8 angles.

The sum of interior angles of octagon are

Sum of interior angles=(n-2)180°

where n is the number of sides

Sum=(8-2)180°=6(180°)=1080°

As octagon is regular implies all interior angles are congruent.

So, the measure of the interior angle of a regular octagon is

$=\frac{\text{Sum of interior angles}}{\text{Number of sides}}=\frac{1080}{6}=135^{\circ}$

Hence, the measure of the interior angle of a regular octagon is 135°

Answer 2

Each angle of a regular octagon has a measure of $\boxed{{\mathbf{135^\circ }}}$ .

Further explanation:

A regular octagon is shown in Figure 1.

Now, from Figure 1 it is observed that a regular octagon has 8 sides and 8 angles.

The formula to obtain the sum of the interior angles with side $n$  is given below.

${\text{Sum of interior angles}}=\left({n-2}\right)180^\circ$      …… (1)

Here, regular octagon has 8 sides that is $n=8$ .

Substitute $8$  for $n$  in equation (1) to obtain the sum of interior angle of regular octagon.

$\begin{aligned}{\text{Sum of interior angles}}&=\left({8-2}\right)180^\circ\\&=\left(6\right)180^\circ\\&=1080^\circ\\\end{aligned}$

Therefore, the sum of interior angles of a regular octagon is $1080^\circ$ .

The measure of each interior angle with side $n$  and sum of interior angle $s$  is given below.

${\text{Interior angle}}=\frac{{\text{s}}}{{\text{n}}}$

…… (2)

Now, substitute $8$  for $n$  and $1080$  for $s$  in equation (2) to obtain the measure of each interior angle of a regular octagon.

$\begin{aligned}{\text{interior angle}}&=\frac{{1080^\circ}}{8}\\&=135^\circ\\\end{aligned}$

Therefore, each angle of a regular octagon is $135^\circ$ .

Thus, each angle of a regular octagon has a measure of $\boxed{{\mathbf{135^\circ }}}$ .

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Lines and angles

Keywords: angle, regular octagon, $135$  degree, measure, angle of a regular octagon, $1080$  degree, sum of interior angles.