Advertisements
Advertisements
प्रश्न
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
उत्तर
∵ ∠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.
संबंधित प्रश्न
How many diagonals does following have?
A regular hexagon
Complete of the following, so as to make a true statement:
A quadrilateral has ...... angles.
Complete of the following, so as to make a true statement:
The measure of each angle of a convex quadrilateral is ..... 180°.
In Fig. 16.19, ABCD is a quadrilateral.
How many pairs of adjacent sides are there?
The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.
In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°. Find :
(i) the value of x.
(ii) each angle of the quadrilateral.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.
In the given figure : ∠b = 2a + 15 and ∠c = 3a + 5; find the values of b and c.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; 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.
The diagonals of a rhombus are 6 .cm and 8 cm. State the angle at which these diagonals intersect.
One angle of a hexagon is 140° and the remaining angles are in the ratio 4 : 3 : 4 : 5 : 4. Calculate the measures of the smallest and the largest angles.
One angle of a pentagon is 160° and the rest are all equal angles. Find the measure of the equal angles.
What is the maximum number of obtuse angles that a quadrilateral can have?
Measures of the two angles between hour and minute hands of a clock at 9 O’ clock are ______.
In the following figure, if point A is shifted to point B along the ray PX such that PB = 2PA, then the measure of ∠BPY is ______.
Using the information given, name the right angles in part of figure:
BA ⊥ BD
Draw a rough sketch of a quadrilateral KLMN. State two pairs of adjacent angles.
Which of the following is a key requirement for correctly naming a □ABCD?
