Posted by **Dillon** on Friday, June 22, 2012 at 8:15am.

In Euclidean geometry, the sum of the measures of the interior anglesof a pentagon is 540o. Predict how the sum of the measures of the interior angles of a pentagon would be different in spherical geometry.

- Geometry -
**Reiny**, Friday, June 22, 2012 at 8:40am
consider a triangle on a globe

so that one vertex is at the north pole, another on the intersection of the equator and the prime meridian, and the third on the intersection of the equator and the 90° meridian.

Wouldn't the angle at the pole be 90° as well as the two angles on the equator?

Thus the sum of the angles of the triangle would be 270°

Can you set up some kind of similar argument for a pentagon?

- Geometry -
**Anonymous**, Monday, June 16, 2014 at 1:55pm
In Euclidean geometry, the sum of the measures of the interior angles of a pentagon is 540°. Predict how the sum of the measures of the interior angles of a pentagon would be different in spherical geometry.

## Answer this Question

## Related Questions

Math - In euclidean geometry, the sum of the measures of the interior angles of ...

math - find the sum of the measures of the intieior angles of each polygon. -...

Geometry - What is the sum of the measures of the interior angles of a convex ...

geometry - the measures of the interior angles of a pentagon are 2x, 6x, 4x-6, ...

Geometry - 1. How many sides does a regular polygon have if one exterior angle ...

math - Find the measure of the interior angle in a regular polygon if the ratio ...

Geometry - If one of the interior angles of a pentagon has a measure of 48 ...

Geometry - I don't undestand this question in my geometry textbook. Could nayone...

geometry - If the sum of the measures of the interior angles of a convex n-gon ...

geometry - find the sum of the measures of the interior angles of a 13-gon