Subjects geometry

Interior Angle Sum D15939

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. Let's clarify the step where we calculate $180 \times 5 = 900$.\n\n2. This step comes from the formula for the sum of the interior angles of a polygon: $$\text{Sum of interior angles} = 180(n-2)$$ where $n$ is the number of sides.\n\n3. If $n=7$, then the sum is $$180(7-2) = 180 \times 5 = 900.$$\n\n4. Here, $7-2=5$ is the number of triangles you can divide the polygon into, and each triangle has interior angles summing to 180 degrees.\n\n5. Multiplying $180$ by $5$ gives the total sum of interior angles, which is $900$ degrees.\n\n6. So, the step $180 \times 5 = 900$ is simply multiplying the number of triangles by the sum of angles in each triangle to find the total interior angle sum of the polygon.