Geometry

Question Analysis:
This problem involves mixed exterior angles in a convex polygon.
We use the angle sum rule for exterior angles.
The main focus is on summing multiple given angles and deducing the number of sides.

Key Concept Explanation:
In any convex polygon, the sum of one exterior angle per vertex is always 360°, no matter how many sides or what the individual angle measures are.

Step-by-Step Solution:
Given:
6 angles = 30° each → 6 × 30 = 180°
Let remaining angles be 60°
Let number of 60° angles = x
Total angle sum must be 360°:
180 + 60x = 360
→ 60x = 180
→ x = 3
Total number of sides = 6 (30°) + 3 (60°) = 9 sides

Common Mistakes:
Assuming regular...