# Class 08 - Chapter 03 - Understanding Quadrilaterals (30)

**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

**Q.17. **

**Q.18. **

**Q.19. **

**Q.20. **

**Q.21. **

**Q.22. **

**Find the value of 'x' in the following figures:**

**Q.23. **

**Q.24. **

**Q.25. **

**Q.26. **

**Q.27. **

**Q.28. **

**Q.29. **

**Q.30. **

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