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.
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
ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC.
Define the following term Convex Quadrilateral .
In a quadrilateral, define of the following Vertices .
In a quadrilateral, define of the following Angles .
In a quadrilateral, define of the following Opposite sides .
Complete of the following, so as to make a true statement:
The number of pairs of adjacent angles of a quadrilateral is .......
Complete of the following, so as to make a true statement:
A diagonal of a quadrilateral is a line segment that joins two ...... vertices of the quadrilateral.
Three angles of a quadrilateral are equal. Fourth angle is of measure 150°. What is the measure of equal angles.
The four angles of a quadrilateral are as 3 : 5 : 7 : 9. Find the angles.
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that \[∠COD = \frac{1}{2}(∠A + ∠B) .\]
The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sided of the polygon.
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 ...............
If ABCD is a rectangle with ∠BAC = 32°, find the measure of ∠DBC.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C
From the following figure find;
- x
- ∠ABC
- ∠ACD
Angle A of an isosceles trapezium ABCD is 115°; find the angles B, C and D.
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
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.
A quadrilateral can have all four angles as obtuse.
Measures of the two angles between hour and minute hands of a clock at 9 O’ clock are ______.
If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is ______.
In the given figure.
∠AOD is a/an ____ angle
In given figure, What is BD – BE?
Using the information given, name the right angles in part of figure:
AE ⊥ CE
An angle is said to be trisected, if it is divided into three equal parts. If in the given figure, ∠BAC = ∠CAD = ∠DAE, how many trisectors are there for ∠BAE?
