draw various type of quadrilateral and show that the sum of exterior angles of each quadrilateral in 360 degree
*I known koi answer nahi de paayga aur jo de diya wo mahan*
Answers
Q1. 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
Q2. How many diagonals does each of the following have?
(a) A convex quadrilateral
Ans. Two
(b) A regular hexagon
Ans. 9
(c) A triangle
Ans. 0 (zero)
Q3. What is the sum of the measures of the angles of a convex quadrilateral? Why this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Ans. Angle sum of a convex quadrilateral = (4 – 2) × 180° = 2 × 180° = 360°
Since, quadrilateral, which is not convex, i.e. concave has same number of sides i.e. 4 as a convex quadrilateral have, thus, a quadrilateral which is not convex also hold this property. i.e. angle sum of a concave quadrilateral is also equal to 360°
Q4. 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
Ans. Given number of sides = 7
Angle sum of a polygon with 7 sides
= (7 – 2) × 180° = 5 × 180° = 900°
(b) 8
Ans. Given number of sides = 8
Angle sum of a polygon with 8 sides
= (8 – 2) × 180° = 6 × 180° = 1080°
(c) 10
Ans. Given number of sides = 10
Angle sum of a polygon with 10 sides
= (10 – 2) × 180° = 8 × 180° = 1440°
(d) n
Ans. Given number of sides = 7
Angle sum of a polygon with n sides = (n – 2) × 180° = (n – 2)180°
Q5. What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides (ii) 4 sides
(iii) 6 sides
Ans. A polygon with equal sides and equal angles is called reagular polygon.
(i) Equilateral triangle
(ii) Square
(iii) Regular hexagon
Q6. (a) Find the angle measures x in the following figures.
Ans. We know that, angle sum of a quadrilateral = 360°
∴ 50° + 130° + 120° + x = 360°
⇒ 300° + x = 360°
⇒ x = 360° – 300°
⇒ x = 60° Answer
Q6. (b)
Ans. We know that, angle sum of a quadrilateral = 360°
∴ 90° + 60° + 70° + x = 360°
⇒ 220° + x = 360°
⇒ x = 360° – 220°
⇒ x = 140° Amswer
Q6. (c)
∴ 110° + 120° + 30° + x + x = 540°
⇒ 260° + 2x = 540°
⇒ 2x = 540° – 260°
⇒ 2x = 280°
Q6. (d)
Ans. Angle sum of a pentagon = (5 – 2) x 180°
= 3 × 180° = 540°
Since, it is a regular pentagon, thus, its angles are equal
∴ x + x + x + x + x = 540°
⇒ 5x = 540°
⇒ x = 108° Answer