Opposite Angles in a Parallelogram Are Equal

Q.

In a parallelogram ABCD, if $\angle D={115}^{\circ }$ then write the measure of $\angle A$

Q.

ABCD is a parallelogram in which $\angle A={70}^{\circ }$. Compute $\angle B,\angle C,and\angle D.$

Q.

In a parallelogram ABCD, If $\angle DAB={75}^{\circ }$ and $\angle DBC={60}^{\circ },then\angle BDC=$

1. ${60}^{\circ }$

2. ${75}^{\circ }$

3. ${45}^{\circ }$

4. ${55}^{\circ }$

Q.

In a triangle $\angle ABC,\angle A={50}^{\circ },\angle B={60}^{\circ }and\angle C={70}^{\circ }$. Find the measures of the angles of the triangle formed by joining the mid -points of the sides of this triangle.

Q.

In the given figure, ABCD is a parallelogram in which $\angle BDC={45}^{\circ }and\angle BAD={75}^{\circ }$. Then, $\angle CBD=$ ?

(a) ${45}^{\circ }$

(b) ${55}^{\circ }$

(c) ${60}^{\circ }$

(d) ${75}^{\circ }$

Q.

If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.

Q.

In parallelogram ABCD if $\angle A=(3x-{20}^{\circ }),\angle B=(y+{15}^{\circ }),\angle C=(x+{40}^{\circ })$, then find the value of x and y .

Q.

Find the measure of all the angles of a parallelogram , if one angle is ${24}^{\circ }$ less than twice the smallest angle.

Q. In the given figure, ABCD is parallelogram. If $\angle A={75}^{\circ }$, then $\angle B$ is

1. 
2. 
3. 
4. 

Q.

In the figure , $ABCD$ is a parallelogram in which $\angle DAB={75}^{\circ }and\angle DBC={60}^{\circ }$. Compute $\angle CDBand\angle ADB.$

Q.

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32^o, ∠AOB = 70^o, then ∠DBC is equal to:

1. 32^o

2. 24^o

3. 38^o

4. 88^o

Q.

In the adjoining figure, ABCD is a parallelogram in which $\angle BAD={75}^{\circ }and\angle CBD={60}^{\circ }$. Then, $\angle BDC=$ ?

(a) ${60}^{\circ }$

(b) ${75}^{\circ }$

(c) ${45}^{\circ }$

(d) ${50}^{\circ }$

Q.

ABCD is a rhombus such that $\angle ACB={50}^{\circ }$. Then, $\angle ADB=$ ?

(a) ${40}^{\circ }$

(b) ${25}^{\circ }$

(c) ${65}^{\circ }$

(d) ${130}^{\circ }$

Q.

The bisectors of any two adjacent angles of a parallelogram intersect at

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${90}^{\circ }$

Q.

In the figure , ABCD is a parallelogram in which $\angle A={60}^{\circ }$. If the bisectors of $\angle Aand\angle B$ meet at P, prove that AD =DP, PC =BC and DC = 2AD.

Q.

Diagonals of a quadrilateral ABCD bisect each other. If $\angle A={45}^{\circ }$, then $\angle B=$

1. ${115}^{\circ }$

2. ${120}^{\circ }$

3. ${125}^{\circ }$

4. ${135}^{\circ }$

Q.

ABCD is a paralleologram in which diagonal AC bisects $\angle BAD.$ If $\angle BAC={35}^{\circ }$, then $\angle ABC=$

1. ${70}^{\circ }$

2. ${110}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q. The angles A, B, C and D of a quadrilateral ABCD have measures in the ratio 2 : 4 : 5 : 7. Find the measures of these angles. What type of quadrilateral is it? Give reasons. [4 MARKS]

Q.

In the adjoining figure, ABCD is a parallelogram whose diagonals intersect each other at O. A line segment EOF is drawn to meet AB at E and DC at F. Prove that OE = OF.

Q.

In a parallelogram ABCD, write the sum of angles A and B.

Q.

PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following cases, PQRS is a parallelogram ?

1. $\angle P={100}^{\circ },\angle Q={80}^{\circ },\angle R={100}^{\circ }$

2. $\angle P={85}^{\circ },\angle Q={85}^{\circ },\angle R={95}^{\circ }$

3. PQ = 7 cm, QR = 7 cm, RS = 8 cm, SP = 8 cm

4. OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS = 5.2 cm

Q.

Which of the following is not true for a parallelogram?

(a) Opposite sides are equal.

(b) Opposite angles are equal.

(c) Opposite angles are bisected by the diagonals.

(d) Diagonals bisect each other.

Q.

What special name can be given to a quadrilateral $PQRS$ if $\angle P+\angle S={180}^{\circ }$?

Q.

In a parallelogram ABCD, $\angle D={135}^{\circ },$ determine the measure of $\angle Aand\angle B$.

Q.

If ABCD is a rhombus with $\angle ABC={56}^{\circ }$, find the measure of $\angle ACD$.

Q.

In the adjoining figure, ABCD is a parallelogram in which $\angle A={72}^{\circ }$. Calculate $\angle B,\angle Cand\angle D$.

Q.

There is a theorem in parallelogram where opposite angles are equal, prove it.

Q.

In a parallelogram ABCD, if $\angle B={135}^{\circ }$ , determine the meaures of its other angles.

Q.

In a quadrilateral PQRS, the diagonals PR and QS bisect each other. If $\angle Q={56}^{\circ }$, determine $\angle R$.

Q.

If measures opposite angles of a parallelogram are $(60-x{)}^{\circ }and(3x-4{)}^{\circ },$ then find the measures of angles of the parallelogram.