Question

Geometry math question please help

Answer 1

To find one interior angle of a regular octagon first we need to find the sum of all interior angles of the octagon.

There is a formula to find the sum of all interior angles. The formula is

$(n-2)180^o$, where n is the total number of sides of the polygon.

For octagon the total number of sides = 8.

So the sum of interior angles of the octagon

= $(8-2)180^o$

= $(6)(180^o)$

= $1080^o$

Now for regular octagon all the angles are equal.

There are total of 8 angles for the octagon. As all angles are same, we can find one interior angle by dividing the sum of interior angles by the number of angles.

So, the measurement of one interior angle

= $\frac{(1080^o)}{8}$

= $135^o$

We have got the required answer here. The measure of one interior angle of regular octagon is $135^o$.

So, the correct option is option D.