Angles of a Parallelogram

Q. In the following figure ABCD and PQRS are parallelograms. Find the measure of x.

1. 40${}^{\circ }$
2. 50${}^{\circ }$
3. 60${}^{\circ }$
4. 70${}^{\circ }$

Q.

Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

Q.

Two adjacent angles of a parallelogram are $(2x+25{)}^{\circ }and(3x-5{)}^{\circ }$. The value of x is

(a) 28 (b) 32 (c) 36 (d) 42

Q.

The sum of two opposite angles of a parallelogram is ${130}^{\circ }$. Find the measure of each of its angles.

Q.

Two adjacent angles of a parallelogram are $(3x-4{)}^{\circ }and(3x+16{)}^{\circ }$. Find the value of x and hence find the measure of each of its angles.

Q.

In the figure, $ABCD$ and $AEFG$ are parallelograms. If $\angle C={55}^{\circ },$ what is the measure of $\angle F?$

Q.

The angle between the altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is ${60}^{\circ }$.
Find the angles of the parallelogram.

Q.

A 6 sided regular polygon (hexagon) is inscribed in a circle of radius 10 cm, find area of the hexagon. [2 MARKS]

Q.

In the adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the geometrical truths you use to find them.

Q.

The ratio of two sides of a parallelogram is as 3:5, and its perimeter is 48 m, then the sides of the parallelogram are

1. 32m and 34m

2. 9m and 15m

3. 15m and 35m

4. 9m and 45m

Q.

$\text{In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD.}\text{Prove that :}\left(i\right)AE=AD.\left(ii\right)\text{DE bisects and}\angle ADCand\left(iii\right)\text{Angle DEC is a right angle.}$

Q.

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

Q.

$\text{In parallelogram ABCD,}\angle A=3times\angle B.$

$\text{Find all the angles of the parallelogram.}$

$\text{In the same parallelogram, ~if}AB=5x-7and$

$CD=3x+1;\text{find the length of CD.}$

Q.

Question 84(i)

What is the type of other angles of a linear pair, if one of its angles is acute?

Q.

In a parallelogram ABCD, the diagonals bisect each other at O. If $\angle ABC={30}^{\circ },\angle BDC={10}^{\circ }and\angle CAB={70}^{\circ }$.

Find: $\angle DAB,\angle ADC,\angle BCD,\angle AOD,\angle DOC,\angle BOC,\angle AOB,\angle ACD,\angle CAB,\angle ADB,\angle ACB,\angle DBCand\angle DBA$.

Q.

$\text{In parallelogram PQRS,}\angle Q=(4x-5{)}^{\circ }and\angle S=(3x+10{)}^{\circ }.\text{Calculate :}\angle Qand\angle R.$

Q. Question 31
If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measures of the angles are
a) ${72}^{\circ },{108}^{\circ }$
b) ${36}^{\circ },{54}^{\circ }$
c) ${80}^{\circ },{120}^{\circ }$
d) ${96}^{\circ },{144}^{\circ }$

Q. In the following figure RUNS is a parallelogram. Find x and y.

1. $x=43,y=27$
2. $x=27,y=43$
3. $x=23,y=47$
4. $x=47,y=23$

Q.

Find the angles marked with a question mark shown in the figure.

Q.

Prove that diagonals of a parallelogram bisect each other.

Q.

If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as __________.

Q.

$\text{Use the information given in the alongside diagram to find the value of x, y and z.}$

Q. Question 3 (iii)
Can a quadrilateral ABCD be a parallelogram, if:
(iii) $\angle A={70}^{\circ }and\angle C={65}^{\circ }$

Q. Question 6
Two adjacent angles of a parallelogram have equal measure. Find the measure of the angles of the parallelogram.

Q.

Two adjacent angles of a parallelogram are as 1:2 Find the measure of all the angles of the parallelogram.

Q. Question 149
In parallelogram FIST, find $\angle SFT,\angle OST$ and $\angle STO$.

Q.

If an angle of a parallelogram is two-third of its adjacent angle , the smallest angle of the parallelogram is

(a) ${54}^{\circ }$ (b) ${72}^{\circ }$

(c)${81}^{\circ }$ (d) ${108}^{\circ }$

Q. Question 35
In the given figure, ABCD and BDCE are parallelograms with common base DC. If $BC\perp BD$, then $\angle BEC$ is equal to
a) ${60}^{\circ }$
b) ${30}^{\circ }$
c) ${150}^{\circ }$
d) ${120}^{\circ }$

Q.

The sum of adjacent angles of a parallelogram is
a) ${180}^{\circ }$
b) ${120}^{\circ }$
c) ${360}^{\circ }$
d) ${90}^{\circ }$

Q. Question 180
ABCD is a parallelogram. Point P and Q are taken on the sides AB and AD, respectively and the parallelogram PRQA is formed. If $\angle C={45}^{\circ }$, find $\angle R$.