Question

kyla claims that the sum of the interior angles of any closed figure is 360 degrees or greater. which figure is a counterexample to kylas claim?

Explanation:

Step1: Recall angle - sum formula

The sum of interior angles of a polygon is given by the formula $(n - 2)\times180^{\circ}$, where $n$ is the number of sides of the polygon.

Step2: Calculate for hexagon

For a hexagon, $n = 6$. Then $(n - 2)\times180^{\circ}=(6 - 2)\times180^{\circ}=4\times180^{\circ}=720^{\circ}$.

Step3: Calculate for triangle

For a triangle, $n = 3$. Then $(n - 2)\times180^{\circ}=(3 - 2)\times180^{\circ}=1\times180^{\circ}=180^{\circ}$.

Step4: Calculate for rectangle

For a rectangle (a type of quadrilateral), $n = 4$. Then $(n - 2)\times180^{\circ}=(4 - 2)\times180^{\circ}=2\times180^{\circ}=360^{\circ}$.

Step5: Calculate for octagon

For an octagon, $n = 8$. Then $(n - 2)\times180^{\circ}=(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$.

Answer:

The triangle, since its sum of interior angles is $180^{\circ}<360^{\circ}$ and serves as a counter - example to Kyla's claim.