Formual to find the number of triangles formed by line at given angles
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I assume you are drawing all the non-overlapping triangles generated by drawing all possible diagonals from a single vertex. For example, let’s say you have a hexagon. It has 6 sides and 6 vertices. Pick one vertex. Draw a diagonal from that vertex to all the other vertices. There will not be 6 diagonals because you can’t draw to the vertex you have chosen, and you can’t draw to the vertices on either side of that one because you would be drawing along a side. So there must be 6–3 = 3 diagonals. The three diagonals split the inside of the polygon into 4 triangles.
No matter how many sides the polygon has, you have 3 fewer diagonals than sides because there are 3 vertices you can’t use. And you will have 1 more triangle than there are diagonals. A 72 sided polygon would therefore have 69 diagonals and 70 triangles. If you are using this to find the sum of the interior angles in the polygon, simply multiply the number of triangles by 180. (70 x 180 = 12600 (degrees).)
So for a polygon with n sides, there are n-2 triangles, assuming the triangles I described are the ones you are talking about. And the sum of the interior angles will be (n-2)180.
I wouldn’t bother learning this as a formula as you will never remember it if you haven’t used it recently. Just understand the process and reconstruct it when you need it.
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I assume you are drawing all the non-overlapping triangles generated by drawing all possible diagonals from a single vertex. For example, let’s say you have a hexagon. It has 6 sides and 6 vertices. Pick one vertex. Draw a diagonal from that vertex to all the other vertices. There will not be 6 diagonals because you can’t draw to the vertex you have chosen, and you can’t draw to the vertices on either side of that one because you would be drawing along a side. So there must be 6–3 = 3 diagonals. The three diagonals split the inside of the polygon into 4 triangles.
No matter how many sides the polygon has, you have 3 fewer diagonals than sides because there are 3 vertices you can’t use. And you will have 1 more triangle than there are diagonals. A 72 sided polygon would therefore have 69 diagonals and 70 triangles. If you are using this to find the sum of the interior angles in the polygon, simply multiply the number of triangles by 180. (70 x 180 = 12600 (degrees).)
So for a polygon with n sides, there are n-2 triangles, assuming the triangles I described are the ones you are talking about. And the sum of the interior angles will be (n-2)180.
I wouldn’t bother learning this as a formula as you will never remember it if you haven’t used it recently. Just understand the process and reconstruct it when you need it.
HOPE THIS ANSWER HELPS YOU
MARK AS BRAINLIEST ✌✌
_______×××××_______
krishna6889:
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