NCERT Solutions Class 8 Maths Chapter 11 — Geometric Explorations

Solution:

Step 1: A polygon can be divided into (n-2) non-overlapping triangles by drawing diagonals from one vertex.

Step 2: Since the sum of interior angles of one triangle is 180°, the sum of interior angles of a polygon with 'n' sides is (n-2) times 180°. [Sum = (n - 2) × 180°]

Solution:

Step 1: For any convex polygon, if you traverse its perimeter and turn at each vertex by its exterior angle, you complete one full circle.

Step 2: A full circle represents a total rotation of 360°. Therefore, the sum of the exterior angles of any convex polygon is always 360°.

Solution:

Step 1: The sum of the interior angles of any quadrilateral is 360°.

Step 2: Let the unknown fourth angle be 'x'. So, 70° + 95° + 110° + x = 360°.

Step 3: Adding the known angles: 275° + x = 360°.

Step 4: Subtracting 275° from both sides: x = 360° - 275° = 85°.

Solution:

Step 1: One of the key properties of a parallelogram is that its opposite angles are equal.

Step 2: In parallelogram ABCD, ∠A and ∠C are opposite angles.

Step 3: Therefore, if ∠A = 65°, then ∠C must also be 65°.

Solution:

Step 1: The definition provided describes a polygon.

Step 2: A circle, oval, and semicircle are all curved shapes, not made up of only line segments.

Step 3: A triangle is a three-sided polygon, formed by three straight line segments connected end-to-end to form a closed figure.