Best Answer

The short answer is "They Don't!"

First we must understand what a convention is. A convention is simply an agreement that we all follow. Sometimes there are many conventions. E.g. We measure speed in kph, mph, mach and knots to name a few. In some cases the whole world agrees on a single convention.

By convention a circle is divided into 360 slices, each slice is called "one degree". Thus a circle is divided into 360 degrees and now we have a tool to measure angles. This convention is world wide.

A square is a square because it has 4 equal sides and 4 equal corners. To measure a square or any polygon, we move along the boundary and using our measuring device we measure every change of direction. A square measures 360 degrees.

If we measure a circle using the same rules that we apply to polygons we must start at a point on the circumference and measure each change of direction. A circle is always changing, thus we can say that a circle has an infinite number of changes of direction. Each change is infinitely close to 180 degrees. Thus a circle has an infinite number of degrees when measured using the same rules that we apply to polygons.

Consider the following test given by teachers to children.

How many degrees in a triangle___________________Answer___180

How many degrees in a square____________________Answer___360

How many degrees in a hexagon__________________Answer___720

How many degrees in a octagon__________________Answer___1080

How many degrees in a circle____________________Answer___Infinity

This test sets up a mathematical progression for young minds to solve. The answer to the last question is not 360. It is in fact infinity.

If a teacher wants an answer of 360 then the question should be a separate question such as "how many degrees is a circle divided into?

Q: Why does the square and the circle's angles add up to 360 degrees?

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Continue Learning about Other Math

All internal angles of a quadrilateral like a square sum to 360 degrees.

The interior angles of a square sum to 360 degrees.

A square has 4 right angles. Right angles are 90 degree angles.4*90 degrees = 360 degrees

360 degrees

The sum of the interior angles in a square is 90 degrees per corner times 4 corners. 4x90=360. 360 degrees is the sum of interior angles in a square, or rectangle, for that matter.

Related questions

The angles around circles add up to 360 degrees

360 degrees in a circle

All internal angles of a quadrilateral like a square sum to 360 degrees.

Because there are 360 degrees around a circle and a complete rotation of an angle is also 360 degrees

The interior angles of a square sum to 360 degrees.

Protractors have to be half- circles because they measure angles less than 360 degrees.

The degrees of a square is 360 degrees. A square has four equal angles, each measuring 90 degrees.

The 4 equal angles of 90 degrees within a square add up to 360 degrees

The interior angles of a square or any rectangle add up to 360 degrees.

A square has 4 right angles. Right angles are 90 degree angles.4*90 degrees = 360 degrees

A square has 4 90 degree angles in the inside. The sum of all the inside angles of a square is 360 degrees.

360 degrees