Q.1. State whether the following statements are true or false:
(a) A simple open curve made up of only line segments is called a polygon.
(b) A diagonal is a line segment connecting two consecutive vertices of a polygon.
(c) Some diagonals of a concave polygons lie outside the polygon.
(d) Regular polygon is either 'equiangular' or 'equilateral'.
(e) Right angled triangle is a regular polygon.
(f) The sum of the measures of the external angles of any polygon is 360°.
Q.2. How many diagonals does each of the following have?
(a) a regular quadrilateral (b) a regular pentagon (c) a regular heptagon (d) a triangle
Q.3. What is the sum of the measures of the angles of the following:
(a) a triangle (b) a quadrilateral (c) a pentagon
Q.4. What is the sum of the measures of the angles of the polygons with number of sides as follows:
(a) 3 (b) 10 (c) 20 (d) 15 (e) 8
Q.5. Find the number of sides of a regular polygon whose each exterior angle has a measure of:
(a) 30° (b) 45° (c) 60° (d) 90°
Q.6. Find the measure of exterior angle of a regular polygon whose number of sides is equal to:
(a) 18 (b) 9 (c) 10 (d) 20
Q.7. Find the minimum interior angle possible for a regular polygon?
Q.8. Find the maximum interior angle possible for a regular polygon?
Q.9. Explain how a square is a parallelogram.
Q.10. Name the quadrilaterals whose diagonals bisect each other.
Q.11. Name the quadrilaterals whose diagonals are perpendicular bisectors of each other.
Q.12. Name the quadrilaterals whose diagonals are equal.
Q.13. Name the quadrilaterals that have four sides of equal length.
Q.14. Name the quadrilaterals that have four right angles.
Q.15. Explain why a parallelogram is a convex quadrilateral.
Q.16. How many diagonals does each of the following have:
(a) a regular polygon with n sides (b) a regular pentagon (c) a regular octagon (d) a regular decagon
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
Find the value of 'x' in the following figures:
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