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Page 1
Q u e s t i o n : 5
Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Find the measure of each angle of the
parallelogram.
S o l u t i o n :
It is given that the two opposite angles of a parallelogram are and .
We know that the opposite angles of a parallelogram are equal.
Therefore,
Page 2
Q u e s t i o n : 5
Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Find the measure of each angle of the
parallelogram.
S o l u t i o n :
It is given that the two opposite angles of a parallelogram are and .
We know that the opposite angles of a parallelogram are equal.
Therefore,
…… i
Thus, the given angles become
Also, .
Therefore the sum of consecutive interior angles must be supplementary.
That is;
Since opposite angles of a parallelogram are equal.
Therefore,
And
Hence the four angles of the parallelogram are , , and .
Q u e s t i o n : 6
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
S o l u t i o n :
Let one of the angle of the parallelogram as
Then the adjacent angle becomes
We know that the sum of adjacent angles of the parallelogram is supplementary.
Therefore,
Thus, the angle adjacent to
Page 3
Q u e s t i o n : 5
Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Find the measure of each angle of the
parallelogram.
S o l u t i o n :
It is given that the two opposite angles of a parallelogram are and .
We know that the opposite angles of a parallelogram are equal.
Therefore,
…… i
Thus, the given angles become
Also, .
Therefore the sum of consecutive interior angles must be supplementary.
That is;
Since opposite angles of a parallelogram are equal.
Therefore,
And
Hence the four angles of the parallelogram are , , and .
Q u e s t i o n : 6
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
S o l u t i o n :
Let one of the angle of the parallelogram as
Then the adjacent angle becomes
We know that the sum of adjacent angles of the parallelogram is supplementary.
Therefore,
Thus, the angle adjacent to
Since, opposite angles of a parallelogram are equal.
Therefore, the four angles in sequence are , , and .
Q u e s t i o n : 7
Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle.
S o l u t i o n :
Let the smallest angle of the parallelogram be
Therefore, according to the given statement other angle becomes .
Also, the opposite angles of a parallelogram are equal.
Therefore, the four angles become , , and .
According to the angle sum property of a quadrilateral:
Thus, the other angle becomes
Hence, the four angles of the parallelogram are , , and .
Q u e s t i o n : 8
The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm what is the measure of the shorter
side?
S o l u t i o n :
Let the shorter side of the parallelogram be cm.
The longer side is given as cm.
Perimeter of the parallelogram is given as 22 cm
Therefore,
Hence, the measure of the shorter side is cm.
Page 4
Q u e s t i o n : 5
Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Find the measure of each angle of the
parallelogram.
S o l u t i o n :
It is given that the two opposite angles of a parallelogram are and .
We know that the opposite angles of a parallelogram are equal.
Therefore,
…… i
Thus, the given angles become
Also, .
Therefore the sum of consecutive interior angles must be supplementary.
That is;
Since opposite angles of a parallelogram are equal.
Therefore,
And
Hence the four angles of the parallelogram are , , and .
Q u e s t i o n : 6
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
S o l u t i o n :
Let one of the angle of the parallelogram as
Then the adjacent angle becomes
We know that the sum of adjacent angles of the parallelogram is supplementary.
Therefore,
Thus, the angle adjacent to
Since, opposite angles of a parallelogram are equal.
Therefore, the four angles in sequence are , , and .
Q u e s t i o n : 7
Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle.
S o l u t i o n :
Let the smallest angle of the parallelogram be
Therefore, according to the given statement other angle becomes .
Also, the opposite angles of a parallelogram are equal.
Therefore, the four angles become , , and .
According to the angle sum property of a quadrilateral:
Thus, the other angle becomes
Hence, the four angles of the parallelogram are , , and .
Q u e s t i o n : 8
The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm what is the measure of the shorter
side?
S o l u t i o n :
Let the shorter side of the parallelogram be cm.
The longer side is given as cm.
Perimeter of the parallelogram is given as 22 cm
Therefore,
Hence, the measure of the shorter side is cm.
Q u e s t i o n : 9
In a parallelogram ABCD, ?D = 135°, determine the measures of ?A and ?B.
S o l u t i o n :
It is given that ABCD is a parallelogram with
We know that the opposite angles of the parallelogram are equal.
Therefore,
Also, and are adjacent angles, which must be supplementary.
Therefore,
Hence , and .
Q u e s t i o n : 1 0
ABCD is a parallelogram in which ?A = 70°. Compute ?B, ?C and ?D.
S o l u t i o n :
It is given that ABCD is a parallelogram with
We know that the opposite angles of the parallelogram are equal.
Therefore,
Also, and are adjacent angles, which must be supplementary.
Therefore,
Also, and are opposite angles of a parallelogram.
Therefore,
Page 5
Q u e s t i o n : 5
Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Find the measure of each angle of the
parallelogram.
S o l u t i o n :
It is given that the two opposite angles of a parallelogram are and .
We know that the opposite angles of a parallelogram are equal.
Therefore,
…… i
Thus, the given angles become
Also, .
Therefore the sum of consecutive interior angles must be supplementary.
That is;
Since opposite angles of a parallelogram are equal.
Therefore,
And
Hence the four angles of the parallelogram are , , and .
Q u e s t i o n : 6
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
S o l u t i o n :
Let one of the angle of the parallelogram as
Then the adjacent angle becomes
We know that the sum of adjacent angles of the parallelogram is supplementary.
Therefore,
Thus, the angle adjacent to
Since, opposite angles of a parallelogram are equal.
Therefore, the four angles in sequence are , , and .
Q u e s t i o n : 7
Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle.
S o l u t i o n :
Let the smallest angle of the parallelogram be
Therefore, according to the given statement other angle becomes .
Also, the opposite angles of a parallelogram are equal.
Therefore, the four angles become , , and .
According to the angle sum property of a quadrilateral:
Thus, the other angle becomes
Hence, the four angles of the parallelogram are , , and .
Q u e s t i o n : 8
The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm what is the measure of the shorter
side?
S o l u t i o n :
Let the shorter side of the parallelogram be cm.
The longer side is given as cm.
Perimeter of the parallelogram is given as 22 cm
Therefore,
Hence, the measure of the shorter side is cm.
Q u e s t i o n : 9
In a parallelogram ABCD, ?D = 135°, determine the measures of ?A and ?B.
S o l u t i o n :
It is given that ABCD is a parallelogram with
We know that the opposite angles of the parallelogram are equal.
Therefore,
Also, and are adjacent angles, which must be supplementary.
Therefore,
Hence , and .
Q u e s t i o n : 1 0
ABCD is a parallelogram in which ?A = 70°. Compute ?B, ?C and ?D.
S o l u t i o n :
It is given that ABCD is a parallelogram with
We know that the opposite angles of the parallelogram are equal.
Therefore,
Also, and are adjacent angles, which must be supplementary.
Therefore,
Also, and are opposite angles of a parallelogram.
Therefore,
Hence, the angles of a parallelogram are , , and .
Q u e s t i o n : 1 1
In the given figure, ABCD is a parallelogram in which ?DAB = 75° and ?DBC = 60°. Compute ?CDB and ?ADB.
S o l u t i o n :
The figure is given as follows:
It is given that ABCD is a parallelogram.
Thus
And are alternate interior opposite angles.
Therefore,
…… i
We know that the opposite angles of a parallelogram are equal. Therefore,
Also, we have
Therefore,
…… ii
In
By angle sum property of a triangle.
From i
and ii
,we get:
Hence, the required value for is
And is .
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FAQs on Quadrilaterals- 2 RD Sharma Solutions - Mathematics (Maths) Class 9
| 1. What are the properties of a quadrilateral? |  |
Ans. A quadrilateral is a polygon with four sides. The properties of a quadrilateral include:
1. The sum of the interior angles of a quadrilateral is equal to 360 degrees.
2. The opposite angles of a quadrilateral are equal.
3. The opposite sides of a quadrilateral are parallel.
4. The diagonals of a quadrilateral bisect each other.
5. The consecutive angles of a quadrilateral are supplementary.
| 2. How many types of quadrilaterals are there? | |
Ans. There are several types of quadrilaterals based on their properties. Some common types of quadrilaterals are:
1. Parallelogram: A quadrilateral with opposite sides parallel.
2. Rectangle: A quadrilateral with all angles equal to 90 degrees.
3. Square: A quadrilateral with all sides and angles equal.
4. Rhombus: A quadrilateral with all sides equal.
5. Trapezium: A quadrilateral with one pair of opposite sides parallel.
| 3. How can we determine if a quadrilateral is a parallelogram? | |
Ans. To determine if a quadrilateral is a parallelogram, we need to check its properties. A quadrilateral is a parallelogram if:
1. Opposite sides are parallel.
2. Opposite angles are equal.
3. Diagonals bisect each other.
| 4. What is the interior angle sum of a quadrilateral? | |
Ans. The interior angle sum of a quadrilateral is always equal to 360 degrees. This means that if we measure all four angles of a quadrilateral and add them together, the total sum will always be 360 degrees.
| 5. How can we find the area of a quadrilateral? | |
Ans. The formula to find the area of a quadrilateral depends on its type. Some common formulas to find the area of different types of quadrilaterals are:
1. Parallelogram: Area = base × height
2. Rectangle: Area = length × width
3. Square: Area = side × side
4. Rhombus: Area = (diagonal1 × diagonal2) / 2
5. Trapezium: Area = (sum of parallel sides × height) / 2
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Nov 22, 2024 Last updated |
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