Question

1.5 triangles
score: 9.33/16 answered: 11/16
question 13
the sum of the interior angles of a convex polygon is 1440°. determine how many sides the polygon has.
sides

Explanation:

Step1: Recall the formula for the sum of interior angles

The formula for the sum of interior angles of a convex polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides.

Step2: Substitute the given sum into the formula

We are given \(S = 1440^{\circ}\), so \(1440=(n - 2)\times180\).

Step3: Solve for \(n\)

Divide both sides by \(180\): \(\frac{1440}{180}=n - 2\).
\(8=n - 2\).
Add \(2\) to both sides: \(n=8 + 2\).

Answer:

\(10\)