Advertisements
Advertisements
प्रश्न
The following figure shows a quadrilateral in which sides AB and DC are parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.
Advertisements
उत्तर
Let ∠A = 4x
∠D = 5x
Since ∠A + ∠D = 180° [AB||DC]
4x + 5x = 180°
⇒ 9x = 180°
⇒ x = 20°
∠A = 4 (20) = 80°,
∠D = 5 (20) = 100°
Again ∠B + ∠C = 180° [ AB||DC]
3x – 15° + 4x + 20° = 180°
7x = 180° – 5°
⇒ 7x = 175°
⇒ x = 25°
∠B = 75° – 15° = 60°
and ∠C = 4 (25) + 20 = 100°+ 20°= 120°
संबंधित प्रश्न
In a quadrilateral, define of the following Interior .
Complete of the following, so as to make a true statement:
A quadrilateral is convex if, for each side, the remaining ______ lie on the same side of the line containing the side.
A quadrilateral has all its four angles of the same measure. What is the measure of each?
The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?
In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.
In the given figure, ABCD is a trapezium. Find the values of x and y.
Complete the following statement by means of one of those given in brackets against each:
If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ...............
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 =
In the given figure : ∠b = 2a + 15 and ∠c = 3a + 5; find the values of b and c.
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.
One diagonal of a rectangle is 18 cm. What is the length of its other diagonal?
What is the maximum number of obtuse angles that a quadrilateral can have?
A quadrilateral can have all four angles as obtuse.
Number of angles less than 180° in the following figure is ______ and their names are ______.
The common part between the two angles BAC and DAB in the following figure is ______.
In the following figure, What is BD – DE?
An angle is said to be trisected, if it is divided into three equal parts. If in the following figure, ∠BAC = ∠CAD = ∠DAE, how many trisectors are there for ∠BAE?
Draw a rough sketch of a quadrilateral KLMN. State two pairs of adjacent angles.
Which of the following represents the vertices of quadrilateral ABCD?
