Example Question - number of vertices
Here are examples of questions we've helped users solve.
Polygon Diagonals and Triangles
The image shows a convex polygon, and the question asks, "How many triangles are formed by drawing all the diagonals from a single vertex?" To solve this, you can count the number of sides (vertices) of the polygon and then use the following formula to find the number of triangles formed: Number of triangles formed from one vertex = Number of vertices (n) - 2 However, I cannot visually determine the exact number of sides of the polygon from the image provided. To count the number of sides (vertices), you should start at one corner and move around the polygon, counting each corner until you end up at the starting corner again. If you can provide the number of sides, I can help you calculate the number of triangles.
Solving for Number of Sides in a Regular Polygon
To solve this problem, you can use the formula that relates the number of sides of a regular polygon (n) to the measure of its interior angles (A): \[ A = \frac{(n - 2) \times 180°}{n} \] Given that \( A = 140° \), you will need to set up the equation to solve for n: \[ 140° = \frac{(n - 2) \times 180°}{n} \] Multiply both sides by n to clear the fraction: \[ 140n = (n - 2) \times 180 \] Distribute the 180° across the (n - 2): \[ 140n = 180n - 360 \] Then, subtract 180n from both sides to solve for n: \[ -40n = -360 \] Divide both sides by -40: \[ n = \frac{-360}{-40} \] \[ n = 9 \] Therefore, the regular polygon has 9 sides.
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