CBSE · NCERT · Class 8 Maths · Chapter 3

NCERT Solutions: Class 8 Maths Chapter 3 - Understanding Quadrilaterals

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Chapter-wise NCERT intext questions and exercise answers for Understanding Quadrilaterals, grounded in the official textbook.

Questions are taken verbatim from the NCERT textbook; answers were grounded against the chapter's content during generation. Items needing review are marked.
Sections in this chapter
Exercises 8
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1Exercises8 questions
Q.1What is a polygon? Give examples of polygons and non-polygons.v
Answer:

A polygon is a simple closed curve made only of line segments. Triangles, quadrilaterals and pentagons are polygons; a circle, an open curve and a curve with a curved side are not polygons.

Q.2What is the sum of the measures of the exterior angles of any polygon?v
Solution

Taking one exterior angle at each vertex while walking around the polygon makes one complete turn.

Answer:

$360^\circ$.

Q.3Find the measure of each exterior angle of a regular hexagon.v
Solution

A regular hexagon has 6 equal exterior angles. Each is $360^\circ/6=60^\circ$.

Answer:

$60^\circ$.

Q.4Find the measure of each interior angle of a regular octagon.v
Solution

Each exterior angle is $360^\circ/8=45^\circ$, so each interior angle is $180^\circ-45^\circ=135^\circ$.

Answer:

$135^\circ$.

Q.5What properties distinguish a parallelogram?v
Answer:

Opposite sides are parallel and equal, opposite angles are equal, adjacent angles are supplementary, and diagonals bisect each other.

Q.6State the special properties of a rectangle.v
Answer:

A rectangle is a parallelogram with four right angles. Its opposite sides are equal and parallel, and its diagonals are equal and bisect each other.

Q.7State the special properties of a rhombus.v
Answer:

A rhombus is a parallelogram with all sides equal. Its diagonals bisect each other at right angles and bisect the vertex angles.

Q.8State the special properties of a square.v
Answer:

A square has all sides equal and all angles $90^\circ$. Its diagonals are equal, perpendicular bisectors of each other, and bisect the angles.