Question
In the adjoining figure, $ABCD$ is a parallelogram in which $\angle\text{DAB}=80^{\circ}$ and $\angle\text{DBC}=60^{\circ}.$ Calculate $\angle\text{CDB}$ and $\angle\text{ADB}.$
✓
Answer
$ABCD$ is a parallelogram, so opposite angles are equal.
$\therefore\angle\text{C}=\angle\text{A}=80^{\circ}$ As $AD\ ||\ BC$ and $BD$ is a transversal.
So, $\angle\text{ADB}=\angle\text{DBC}=60^{\circ}$ [Alternate angles] In $\triangle\text{ABD}$
$\angle\text{A}+\angle\text{ADB}+\angle\text{ABD}=180^{\circ}$
$\Rightarrow80^{\circ}+60^{\circ}+\angle\text{ABD}=180^{\circ}$
$\Rightarrow140^{\circ}+\angle\text{ABD}=180^{\circ}$
$\Rightarrow\angle\text{ABD}=180^{\circ}-140^{\circ}=40^{\circ}$
$\therefore\angle\text{ABC}=\angle\text{ABD}+\angle\text{DBC}$
$=40^{\circ}+60^{\circ}=100^{\circ}$ In a parallelogarm, opposite angles are equal.
So, $\angle\text{ADC}=\angle\text{ABC}=\angle100^{\circ}$
$\therefore\angle\text{CDB}=\angle\text{ADC}-\angle\text{ADB}$
$=100^{\circ}-60^{\circ}=40^{\circ}$ and $\angle\text{ADB}=60^{\circ}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
How many cubic centimetres of iron are there in an open box whose external dimension are $36\ cm, 25\ cm$ and $16.5\ cm$, the iron being $1.5\ cm$ thick throughout? If $1cm^3$ of iron weighs $15g$, find the weight of the empty box in kilograms.
→In the given figure, $\text{POQ}$ is a line. Ray $OR$ is perpendicular to line $PQ. OS$ is another ray lying between rays $OP$ and $OR$. Prove that $\angle R O S=\frac{1}{2}(\angle Q O S-\angle P O S)$.
→→
The difference between inside and outside surfaces of a cylindrical tube $14\ cm$ long, is $88\ cm^2.$ If the volume of the tube is $176\ cm^3$, find the inner and outer radii of the tube.
→The population of Delhi State in different census years is as given below:
Represent the above information with the help of a bar graph.
→|
Census year
|
$1961$
|
$1971$
|
$1981$
|
$1991$
|
$2001$
|
|
Population in Lakhs
|
$30$
|
$55$
|
$70$
|
$110$
|
$150$
|
Two sides of a triangular field are $85 m$ and $154 m$ in length and its perimeter is $324 m.$ Find the area of the field.
→Draw a histogram and the frequency polygon from the following data:
→|
Class interval
|
$20-25$
|
$25-30$
|
$30-35$
|
$35-40$
|
$40-45$
|
$45-50$
|
|
Frequency
|
$30$
|
$24$
|
$52$
|
$28$
|
$46$
|
$10$
|
Find the measure of each angle of a parallelogram, if one of its angles is $30^\circ $ less than twice the smallest angle.
→In the given figure, if $x = y$ and $AB = CB$ then prove that $AE = CD$.
→In the given figure, $O$ is the centre of a circle in which $\angle\text{OAB}=20^\circ$and $\angle\text{OCB}=55^\circ.$ Find
$i. \angle\text{BOC}$
$ii. \angle\text{AOC}$
→$i. \angle\text{BOC}$
$ii. \angle\text{AOC}$