Question

Using activity, prove the following formula for
a) Equilateral triangle
b) Square
c) Regular Pentagon
Number of sides x exterior angle=360​

Answer 1

Step-by-step explanation:

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°