How many right angles are in PENTAGON?

Answer 1

Here are two ways. One practical and one mathematical.

Practically, sketch a pentagon like a house with outward leaning walls. Label the top point A and the B, C, D, E clockwise. Lay your pencil on side EA with the pointy end pointing to the right. Holding the pencil still at A, swing the blunt end down and around until it is lined up along line AB. The sharp end is now pointing up and left. Now hold the part of the pencil at B still and swing the sharp end down until the pencil is lined along BC with the sharp end pointing down. Now hold the pencil at c and swing the blunt end left and down to line up the pencil along side DC. Then hold the pencil still at D and swing the sharp end up and round to the left to line the pencil along DE. Lastly, hold the pencil at E and swing the blunt end up and round to the right until we're back lined up along side EA.

Now you know what to do, Do it again and watch how the pencil turns. It rotates one and a half complete times. That is the sum of the internal angles .. 360 +180 degrees.

So a pentagon has 6 rightangles

in its internal angles.

Mathematically, draw the same pentagon and put a dot near the middle. Now connect each of the five vertices

to the middle dot with straight lines. You have drawn five triangles. Now a triangle has 180 degrees in it and so in that pentagon there a five triangles and so five times 180 degrees altogether. 180 degrees is two righttangles, so we have ten rightangles. However the angles of the five triangles gathered at the centre point were added just to do this process, so they don't count. These five angles make up one complete circle which is four rightangles.

So we have to subtract four from the ten rightangles

we had and arrive at six rightangles

in the pentagon.

Fortunately, the two methods both give a 6 rightangle

answer.

Both methods work for polygons of any shape or size.