Opposite Angles of a Parallelogram Are Equal

Q. In the below given figure of parallelogram, AF and BE are angle bisectors of $\angle A$ and $\angle B$ respectively. Find the measure of $x$.

1. ${90}^{\circ }$
2. ${80}^{\circ }$
3. ${70}^{\circ }$
4. ${60}^{\circ }$

Q.

A square is also a

1. Rhombus

2. Parallelogram

3. Kite

4. none of these

Q. In the following figure, PQRS is a parallelogram.


Find the measure of x${}^{\circ }$ and y${}^{\circ }$.

1. 100${}^{\circ }$ and 80${}^{\circ }$.
2. 70${}^{\circ }$ and 110${}^{\circ }$.
3. 500${}^{\circ }$ and 130${}^{\circ }$.
4. 90${}^{\circ }$ and 120${}^{\circ }$.

Q. In a quadrilateral, if the opposite sides and opposite angles are equal, then the quadrilateral is a .

1. parallelogram
2. polygon
3. triangle

Q.

Find the angles x, y and z in the given parallelogram. [3 MARKS]

Q. Question 3 (i)
Can a quadrilateral ABCD be a parallelogram, if:
$\angle D+\angle B={180}^{\circ }$ ?

Q.

The number of diagonals in an octagon will be

1. 28

2. 20

3. 10

4. 16

Q. In the following figure ABCD is a parallelogram.


Find the measure of x${}^{\circ }$, y${}^{\circ }$ and z${}^{\circ }$?

1. 100${}^{\circ }$, 80${}^{\circ }$ and 80${}^{\circ }$
2. 100${}^{\circ }$, 80${}^{\circ }$ and 100${}^{\circ }$
3. 100${}^{\circ }$, 100${}^{\circ }$ and 80${}^{\circ }$
4. 120${}^{\circ }$, 80${}^{\circ }$ and 90${}^{\circ }$

Q. If two adjacent angles i.e., A and B of the parallelogram ABCD are (3x - 4)${}^{\circ }$ and (3x + 16)${}^{\circ }$ respectively, then the measure of angle C is _____ .

1. 80${}^{\circ }$
2. 60${}^{\circ }$
3. 120${}^{\circ }$
4. 100${}^{\circ }$

Q. The sum of two opposite angles of a parallelogram is 120${}^{\circ }$. Find the measure of each of its angles.

1. 60${}^{\circ }$, 120${}^{\circ }$, 60${}^{\circ }$ and 120.${}^{\circ }$
2. 30${}^{\circ }$, 150${}^{\circ }$, 30${}^{\circ }$ and 150.${}^{\circ }$
3. 90${}^{\circ }$, 45${}^{\circ }$, 60${}^{\circ }$ and 120.${}^{\circ }$
4. 60${}^{\circ }$, 90${}^{\circ }$, 60${}^{\circ }$ and 90.${}^{\circ }$

Q.

Two adjacent angles of a parallelogram are in the ratio $1:5$. Then all the angles of the parallelogram are

1. $30°,150°,30°,150°$

2. $85°,95°,85°,95°$

3. $45°,135°,45°,135°$

4. $30°,180°,30°,180°$

Q.

Match the two columns.

$\begin{array}{cc}Column-I& Column-II\\ A)InaparallelogramABCD& P){68}^{\circ }\\ If\angle D={115}^{\circ },thenthemeasure& \\ of\angle Ais& \\ B)PQRSisasquaresuchthatPR& Q){58}^{\circ }\\ AndSQintersectatO.The& \\ Measureof\angle POQis& \\ C)Thediagonalsofarectangle& R){90}^{\circ }\\ ABCDmeetatO.If\angle BOC={44}^{\circ },& \\ Thenthemeasureof\angle OADis& \\ D)IfABCDisarectanglewith& S){65}^{\circ }\\ \angle BAC={32}^{\circ },thenthemeasureof& \\ \angle DBCis& \end{array}$

Choose the correct option:

1. $\left(A\right)\to p;\left(B\right)\to q;\left(C\right)\to r;\left(D\right)\to s$

2. $\left(A\right)\to s;\left(B\right)\to r;\left(C\right)\to q;\left(D\right)\to p$

3. $\left(A\right)\to s;\left(B\right)\to r;\left(C\right)\to p;\left(D\right)\to q$

4. $\left(A\right)\to r;\left(B\right)\to s;\left(C\right)\to q;\left(D\right)\to p$

Q.

A quadrilateral having two pairs of adjacent sides equal . Name this quadrilateral.

Q. ABCD is a parallelogram and X, Y are the mid-points of sides AB and Cd respectively. Then quadrilateral AXCY is a :

1. Parallelogram
2. Rhombus
3. Square
4. Rectangle

Q.

(a) How many right angles are there in a cubical room?

(b) What should be subtracted from ($\frac{5}{12}+\frac{3}{2}$) to get 2?

[3 MARKS]

Q.

ABCD is an isosceles trapezoid with DC as one of the bases.

$\angle$ D = (x + 60)${}^{\circ }$

$\angle$ B = (4x)${}^{\circ }$

DC = (x – 3) cm

What is the length of DC?

1. 24 cm

2. 21 cm

3. 18 cm

4. 27 cm

Q.

We have a parallelogram ABCD with AC and BD as diagonals. In parallelogram ABCD, $\angle$ABC=${110}^{\circ }$, $\angle$DAC = ${15}^{\circ }$, $\angle$CAB = ${25}^{\circ }$, AB = 5cm and CD = 7cm. Can we construct this parallelogram?

1. With ADC, yes

2. With AC, yes

3. No, it is impossible

4. Yes, of course

Q. Opposite sides and angles of a parallelogram are always equal.

1. False
2. True

Q. What is a parallelogram?

Q. From the following parallelogram, find the value of $\angle$DCB.

1. 115°
2. 65°
3. 125°
4. 45°

Q. Two adjacent angles of a parallelogram are equal. What is the measure of each of the angles?

1. 30°
2. 60°
3. 90°
4. 120°

Q. In the following parallelogram, find the value of $x$.

1. 11°
2. 33°
3. 44°
4. 22°

Q. In a parallelogram, opposite angles are ________ and adjacent angles are _________.

1. equal, supplementary
2. supplementary, equal
3. complementary, supplementary
4. equal, complementary

Q.

ABCD is a parallelogram in which $\angle DCB$ and $\angle ABC$ are in ratio 2:7. Find the sum of $\angle ABD$ and $\angle ADB$.

1. ${40}^{\circ }$

2. ${50}^{\circ }$

3. ${70}^{\circ }$

4. ${140}^{\circ }$