Class 8, Maths, Chapter 3, Exercise 3.1, Solutions

Q.1. Given here are some figures:

Classify each of them on the basis of the following.

(a) Simple curve

(b) Simple closed curve

(c) Polygon

(d) Convex polygon

(e) Concave polygon

Ans: (a) Simple curve = (1), (2), (5), (6), (7)

(b) Simple closed curve = (1), (2), (5), (6), (7)

(c) Polygon = (1), (2)

(d) Convex polygon = (2)

(e) Concave polygon = (1)

Q.2. How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle

Ans:

Q.3. What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Ans:

Q.4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides?

(a) 7

(b) 8

(c) 10

(d) n

Ans: we know that, (Side – 2) x 180^{0}

(a) 7

(Side – 2) x 180^{0}

(7 – 2) x 180^{0} = 5 x 180 = 900^{0}

(b) 8

(8 – 2) x 180^{0} = 6 x 180 = 1080^{0}

(c) 10

(10 – 2) x 180^{0} = 8 x 180 = 1260^{0}

(d) n

(n – 2) x 180^{0} = n x 180^{0}

Q.5. (a) What is a regular polygon?

(b) State the name of a regular polygon of

(i) 3 sides

(ii) 4 sides

(iii) 6 sides

Ans:

Q.6. Find the angle measure x in the following figures.

NCERT Solutions For Class 8 Maths Chapter 3, Understanding Quadrilaterals (All Exercises)