Geometry polygon problem

[phdgurl]

This is pretty simple, but I'm not understanding the book's explanation. Help please.

Q. What is the measure of 2 of the 8 angles of a regular octagon?

A. 270 degrees (135 degrees x 2)

I guess I don't fully understand the properties of polygons.

[piyushraghav]

Divide the recgular octagon into 8 triangles. Then the measure of the angle at the vertex is 45 (360/8). In each of the triangles, the sum of interior angles is 180, which leaves 135 as the sum of the remaining two angles of the triangles. Since its a regular octagon, Each angle is 135/2. This is just a half angle of the polygon. The other half angle (another 135/2) is from a neighboring triangle. This gives (135/2 + 135/2 = 135) as the value of each of the interior angles. So two interior angles would be 135x2 = 270. Hope this helps!!

[Dr_GMAT]

Great explaination

[smallbee]

Octagon has 8 equal angels (this is the definition and you can prove it from the book). Hence 8X=360 degree -> x =135degree.

sum of 2 angels is 135x2=270degree.

[yuvakris]

The formula for the total measure of the interior angles of any polygon is (n-2)*180, where n is the number of sides of the polygon. Using this formula we can find the total angle and divide by 8.
(8-2)*180=1080.
when 1080/8=135/interior angle.
so for 2 interior angles, it is 270

[Crack_Mat]

Originally Posted by phdgurl

This is pretty simple, but I'm not understanding the book's explanation. Help please.

Q. What is the measure of 2 of the 8 angles of a regular octagon?

A. 270 degrees (135 degrees x 2)

I guess I don't fully understand the properties of polygons.

Friend you can derive this formula:
(n - 2)*PI = S;
S = sum of internal angles of a nth degree polygon.

So for a general octagon you can write S = 6*PI
For a regular Octagon S = 8*theta; as all angle will be equal.
So Sum of two angles = theta + theta = 2*theta = 6/4 * PI = 3/2*180 deg = 270 deg

[phdgurl]

Thanks guys! All very helpful information!

[sksgill]

the sum of angles of all polygon is (n-2)*180

here (8-2)*180
so 6*(180/8
= 135 is the measure of each angle