Advertisements
Advertisements
Question
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
Solution
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°
RELATED QUESTIONS
In a quadrilateral, define of the following Adjacent angles .
In Fig. 16.21, the bisectors of ∠A and ∠B meet at a point P. If ∠C = 100° and ∠D = 50°, find the measure of ∠APB.
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that \[∠COD = \frac{1}{2}(∠A + ∠B) .\]
If the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that ∠C + ∠D = k ∠AOB, then find the value of k.
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
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.
Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
Write two conditions that will make the adjoining figure a square.
Find the angles of a pentagon which are in the ratio 4: 4: 6: 7: 6.
Find the angles of a quadrilateral whose angles are in the ratio 1: 4: 5: 2.
In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ∠QRS = 100°, then ∠TVS =
If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a ______.
Which of the following is not true for a parallelogram?
If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?
In the following figure,
∠COA is a/an ______ angle
In the following figure, What is AE + EC?
