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.
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.
<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
Every angle in a rectangle is 90 degree.
Diagonals of rectangle cut each other into their half.
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.
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.
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