Question

look at this convex polygon. how many triangles are formed by drawing all the diagonals from a single vertex?

Explanation:

Step1: Recall the formula for the number of triangles

The formula for the number of triangles formed by drawing all the diagonals from a single vertex of an \(n -\)sided polygon is \(n - 2\).

Step2: Identify the number of sides of the polygon

The given polygon is a decagon (10 - sided polygon), so \(n=10\).

Step3: Calculate the number of triangles

Substitute \(n = 10\) into the formula \(n - 2\). We get \(10-2=8\).

Answer:

\(8\)