Advertisements
Advertisements
Question
The four angles of a quadrilateral are as 3 : 5 : 7 : 9. Find the angles.
Advertisements
Solution
\[\text{ Let the angles be in the ratio 3x : 5x : 7x : 9x .} \]
\[\text{ Since, the sum of all the angles of a quadrilateral is } 360°, \text{ we have } : \]
\[3x + 5x + 7x + 9x = 360° \]
\[ \Rightarrow 24x = 360° \]
\[ \Rightarrow x = 15° \]
\[\text{ Thus, the angles are } : \]
\[3x = 45° \]
\[5x = 75° \]
\[7x = 105° \]
\[9x = 135° \]
APPEARS IN
RELATED QUESTIONS
In a quadrilateral, define of the following Adjacent sides .
Complete of the following, so as to make a true statement:
The number of pairs of adjacent angles of a quadrilateral is .......
Complete the following statement by means of one of those given in brackets against each:
If opposite angles of a quadrilateral are equal, then it is necessarily a ....................
In the given figure : ∠b = 2a + 15 and ∠c = 3a + 5; find the values of b and c.
The angles A, B, C and D of a trapezium ABCD are in the ratio 3: 4: 5: 6. Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer.
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.
Find the angles of a quadrilateral whose angles are in the ratio 1: 4: 5: 2.
ABCD is a quadrilateral in which AB || DC and AD = BC. Prove that ∠A = ∠B and ∠C = ∠D.
What conclusion can be drawn from part of given figure, if DB is the bisector of ∠ADC?
In quadrilateral PQRS, which pair represents adjacent sides?
