PRACTICE PROBLEMS ON QUADRILATERALS

Question 1 :

Th e angles of a quadrilateral are in the ratio 2 : 4 : 5 : 7. Find all the angles.

Solution :

The four angles are 2x, 4x, 5x and 7x.

Sum of interior angles of quadrilaterals  =  360

2x + 4x + 5x + 7x  =  360

18x  =  360

x  =  360/18  =  20

x  =  20

2x  =  2(20)  =  40

4x  =  4(20)  =  80

5x  =  5(20)  =  100

7x  =  7(20)  =  140

Hence the required angles are 40, 80, 100 and 140.

Question 2 :

In a quadrilateral ABCD, ∠A = 72° and ∠C is the supplementary of ∠A. The other two angles are 2x–10 and x + 4. Find the value of x and the measure of all the angles.

Solution :

<A + <C  =  180

72 + <C  =  180

<C  =  180 - 72

<C  =  108

<B + <D  =  180

2x - 10 + x + 4  =  180

3x - 6  =  180

3x  =  186

x  =  186/3

x  =  62

2x - 10  =  2(62) - 10  =  124 - 10  =  114

x + 4  =  62 + 4  =  66

Hence the required angles are 72, 108, 114 and 66.

Question 3 :

ABCD is a rectangle whose diagonals AC and BD intersect at O. If ∠OAB =46°, find ∠OBC

Solution :

Every angle in a rectangle is 90 degree.

Diagonals of rectangle cut each other into their half.

So, 

AO  =  BO

<OBA = <OAB

<OBA = 46° ------- (1)

<ABC = <OBA + <OBC

90° = <46° + <OBC

<OBC = 44°

Question 3 :

The lengths of the diagonals of a Rhombus are 12 cm and 16 cm . Find the side of the rhombus.

Solution :

In rhombus diagonals cut each other at right angles.

In triangle OAB,

AB²  =  OA² + OB²

AB²  =  6² + 8²

AB²  =  36 + 64

AB²  =  100

AB  =  10

Hence the side length of rhombus is 10 cm.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.