Quadrilaterals- 1 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


Q u e s t i o n : 1
Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angles.
S o l u t i o n :
Let the measure of the fourth angles be x°. We know that the sum of the angles of a quadrilateral is 360°.
Therefore,
Hence the measure of the fourth angle is .
Q u e s t i o n : 2
In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angles of
the quadrilateral.
S o l u t i o n :
We have , .
So, let  ,
,
And 
By angle sum property of a quadrilateral, we get:
Also,
And
Similarly,
Page 2


Q u e s t i o n : 1
Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angles.
S o l u t i o n :
Let the measure of the fourth angles be x°. We know that the sum of the angles of a quadrilateral is 360°.
Therefore,
Hence the measure of the fourth angle is .
Q u e s t i o n : 2
In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angles of
the quadrilateral.
S o l u t i o n :
We have , .
So, let  ,
,
And 
By angle sum property of a quadrilateral, we get:
Also,
And
Similarly,
Hence, the four angles are , , and .
Q u e s t i o n : 3
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
 
S o l u t i o n :
We have, .
So, let  ,
,
and 
By angle sum property of a quadrilateral, we get:
Also,
And
Similarly,
Hence, the four angles are , ,  and  .
Q u e s t i o n : 4
In a quadrilateal ABCD, CO and DO are the bisectors of ?C and ?D respectively. Prove that ?COD =
1
2
( ?A + ?B).
Page 3


Q u e s t i o n : 1
Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angles.
S o l u t i o n :
Let the measure of the fourth angles be x°. We know that the sum of the angles of a quadrilateral is 360°.
Therefore,
Hence the measure of the fourth angle is .
Q u e s t i o n : 2
In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angles of
the quadrilateral.
S o l u t i o n :
We have , .
So, let  ,
,
And 
By angle sum property of a quadrilateral, we get:
Also,
And
Similarly,
Hence, the four angles are , , and .
Q u e s t i o n : 3
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
 
S o l u t i o n :
We have, .
So, let  ,
,
and 
By angle sum property of a quadrilateral, we get:
Also,
And
Similarly,
Hence, the four angles are , ,  and  .
Q u e s t i o n : 4
In a quadrilateal ABCD, CO and DO are the bisectors of ?C and ?D respectively. Prove that ?COD =
1
2
( ?A + ?B).
S o l u t i o n :
The quadrilateral can be drawn as follows:
We have CO and DO as the bisectors of angles and  respectively.
We need to prove that .
In ,We have,
 …… I
By angle sum property of a quadrilateral, we have:
Putting in equation I
:
Hence proved.