Question
In the given figure, $\angle\text{ABD}=54^\circ$ and $\angle\text{BCD}=43^\circ,$ calculate
$i. \angle\text{ACD}$
$ii. \angle\text{BAD}$
$iii. \angle\text{BDA}$
$i. \angle\text{ACD}$
$ii. \angle\text{BAD}$
$iii. \angle\text{BDA}$
✓
Answer
$i.$ We know that the angles in the same segment of a circle are equal.
$\text{i.e.},\angle\text{ABD}=\angle\text{ACD}=54^\circ$
$ii.$ We know that the angles in the same segment of a circle are equal.
$\text{i.e.},\angle\text{BAD}=\angle\text{BCD}=43^\circ$
$iii.$ In $\triangle\text{ABD},$ we have:
$\angle\text{BAD}+\angle\text{ADB}+\angle\text{DBA}=180^\circ [$Angle sum property of a triangle$]$
$\Rightarrow\ 43^\circ+\angle\text{ADB}+54^\circ=180^\circ$
$\Rightarrow\ \angle\text{ADB}=(180^\circ-97^\circ)=83^\circ$
$\Rightarrow\ \angle\text{BDA}=83^\circ$
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
The factors of $x^3 - 1 + y^3 + 3xy$ are :
→In the adjoining figure, $O$ is the centre of a circle. Chord $CD$ is parallel to diameter $AB$. If $\angle\text{ABC}=25^\circ,$ calculate $\angle\text{CED}.$ 
→If is given that $\angle X Y Z=64^{\circ}$ and $X Y$ is produced to point $P.$ Draw a figure from the given information. If ray $YQ$ bisects $\angle ZYP$, find $\angle XYQ$ and reflex $\angle QYP$.
→In the given figure, $O$ is the centre of the circle, $BD = OD$ and $\text{CD}\perp\text{AB}.$ Find $\angle\text{CAB}.$ 
→Find the area of a trapezium whose parallel sides are $11\ m$ and $25\ m$ long, and the nonparallel sides are $15\ m$ and $13\ m$ long.
→In $\triangle\text{ABC},$ if $3\angle\text{A}=4\angle\text{B}=6\angle\text{C},$ calculate $\angle\text{A},\angle\text{B}$ and $\angle\text{C}.$
→In the adjoining figure, $\text{ABCD}$ is a parallelogram in which $\angle\text{BAO}=35^{\circ},\angle\text{DAO}=40^{\circ}$ and $\angle\text{COD}=150^{\circ}.$ Calculate
$i. \angle\text{ABO},$
$ii. \angle\text{ODC},$
$iii. \angle\text{ACB},$
$iv. \angle\text{CBD}.$
→$i. \angle\text{ABO},$
$ii. \angle\text{ODC},$
$iii. \angle\text{ACB},$
$iv. \angle\text{CBD}.$
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
$100$ surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabets in the surnames was found as follows :
$i.$ Draw a histogram to depict the given information.
$ii.$ Write the class interval in which the maximum number of surnames lie.
→| Number of letters | Number of surnames |
|---|---|
| $1-4$ | $6$ |
| $4-6$ | $30$ |
| $6-8$ | $44$ |
| $8-12$ | $16$ |
| $12-20$ | $4$ |
$ii.$ Write the class interval in which the maximum number of surnames lie.
In the given figure, $\text{ABCD}$ is a square and $\angle\text{PQR}=90^{\circ}.$ If $PB = QC = DR,$ prove that:
$i. QB = RC$,
$ii. PQ = QR$,
$iii. \angle\text{QPR}=45^{\circ}$
→$i. QB = RC$,
$ii. PQ = QR$,
$iii. \angle\text{QPR}=45^{\circ}$
