# Understanding Quadrilaterals – Class 8.

**Chapter 3 of NCERT/CBSE Class 8 Mathematics is about Understanding Quadrilaterals. Here in this lesson you can find out practice problems from this chapter.**

**CBSE CLASS 8 MATHEMATICSUnderstanding Quadrilaterals – Chapter 3 / Model Questions.Fill in the blanks:**

- A 10 sided polygon is known as ————-
- A line segment connecting two non-consecutive vertices of a polygon is called ———-
- The name of a regular polygon with 4 sides is ———–
- The number of diagonals a regular hexagon have ————
**Answer the following:** - In a parallelogram ABCD, opposite sides are given by 4x – 4 and x -1. Find the value of x?
- Find the sum of all the exterior angles of a triangle?
- In a triangle PQR, the three angles are given by (x + 5), (x + 10) and (3x + 15). Find the value of x?
- Three angles of a quadrilateral are 35, 65 and 128 degrees. Find the measure of the fourth angle?
- In a parallelogram ABCD, if one angle is 70 degree, find all the other angles?
- Find the perimeter of a parallelogram whose sides are given by 6 cm and 12 cm?

**ANSWERS:**

- Decagon
- Diagonals
- Square or Rhombus
- 9 sides
- Since the opposite sides of a parallelogram are of equal measure,

4x – 4 = x – 1

4x – x = -1 + 4

3x = 3

x = 1. - We know that the sum of the measures of the external angles of any polygon is 360 degree. Therefore, sum of all the exterior angles of a triangle is 360 degree.
- By angle sum property of triangles, sum of the three angles = 180 degree

x + 5 + x + 10 + 3x + 15 = 180

5x + 30 = 180

5x = 180 – 30 = 150

x = 150 / 5 = 30 - We know that sum of four angles of a quadrilateral is 360 degree.

Let the fourth angle be x and the other three angles are 35, 65 and 128.

Therefore, 35 + 65 + 128 + x = 360

228 + x = 360

x = 132

Therefore, the measure of fourth angle is 132 degree. - Since the opposite angles of a parallelogram are equal, the measures of 2 angles are 70 degree. Also adjacent angles of a parallelogram are supplementary. Therefore, the other two angles are 110 degree each.
- In a parallelogram the opposite sides have same length.

So perimeter = 6 + 12 + 6 + 12 = 36 cm