Advertisements
Advertisements
Question
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other
(i) Is PS also parallel to QR?
(ii) Assign a special name to quadrilateral PQRS.
Advertisements
Solution
∵ ∠P : ∠Q : ∠R : ∠S = 3: 4: 6: 7
Let ∠P = 3x
∠Q = 4x
∠R = 6x
∠S = 7x
∴ ∠P + ∠Q + ∠R + ∠S = 360°
3x + 4x + 6x + 7x = 360°
20x = 360°
x = 18°
∴ ∠P = 3x = 3 × 18 = 54°
∠Q = 4x = 4 × 18 = 72°
∠R = 6x = 6 × 18 = 108°
∠S = 7x = 7 × 18 = 126°
∠Q + ∠R = 72° + 108° = 180°
or ∠P + ∠S = 54° + 126° = 180°
Hence PQ || SR
As ∠P + ∠Q = 72° + 54° = 126°
Which is ≠ 180°
∴ PS and QR are not parallel.
PQRS is a Trapezium as its one pair of opposite side is parallel.
RELATED QUESTIONS
In a quadrilateral, define of the following Angles .
Complete of the following, so as to make a true statement:
A quadrilateral has ..... vertices, no three of which are .....
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of adjacent angles.
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of opposite angles.
In Fig. 16.19, ABCD is a quadrilateral.
How many pairs of adjacent angles are there?
In the given figure, PQRS is an isosceles trapezium. Find x and y.
Complete the following statement by means of one of those given in brackets against each:
f consecutive sides of a parallelogram are equal, then it is necessarily a ..................
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
Use the following figure to find the value of x
The angles A, B, C and D of a quadrilateral are in the ratio 2 : 3 : 2 : 3. Show this quadrilateral is a parallelogram.
Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.
Observe the figure below and find out their name.
Observe the figure below and find out their name.
The angles of a pentagon are x°, (x - 10)°, (x + 20)°, (2x - 44)° and (2x - 70)°. Find the angles.
One angle of a pentagon is 160° and the rest are all equal angles. Find the measure of the equal angles.
If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a ______.
If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is ______.
In the following figure,
∠AOD is a/an ______ angle
In the following figure, What is AE + EC?
Draw a rough sketch of a quadrilateral KLMN. State two pairs of adjacent angles.
