**Practice Problems on Quadrilaterals :**

Here we are going to see some example problems based on the concept 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,

AB^{2} = OA^{2} + OB^{2}

AB^{2} = 6^{2} + 8^{2}

AB^{2} = 36 + 64

AB^{2} = 100

AB = 10

Hence the side length of rhombus is 10 cm.

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