MCQ
In the adjoining figure, $AB = BC$ and $\angle\text{ABD} = \angle\text{CBD},$ then another angle which measures $30^\circ $ is:
- A$\angle\text{BAD}$
- B$\angle\text{BCA}$
- ✓$\angle\text{BDA}$
- D$\angle\text{BCD}$
✓
Answer
Correct option: C.
$\angle\text{BDA}$
In triangle $ABD$ and $CBD$
$AB = BC$ and $\angle\text{ABD} = \angle\text{CBD},$ (Given)
$BD$ (Common)
Therefore In triangle $ABD$ and $CBD$ are congruent by $SAS$ criteria.
Therefore, $\angle\text{BDA}=30^\circ$ (by $CPCT)$
$AB = BC$ and $\angle\text{ABD} = \angle\text{CBD},$ (Given)
$BD$ (Common)
Therefore In triangle $ABD$ and $CBD$ are congruent by $SAS$ criteria.
Therefore, $\angle\text{BDA}=30^\circ$ (by $CPCT)$
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
Which of the following is a correct statement$?$
→$A, B, C$ are three sets of values of $x;$
$A. 2, 3, 7, 1, 3, 2, 3$
$B. 7, 5, 9, 12, 5, 3, 8$
$C. 4, 4, 11, 7, 2, 3, 4$
Which one of the following statements is correct?
→$A. 2, 3, 7, 1, 3, 2, 3$
$B. 7, 5, 9, 12, 5, 3, 8$
$C. 4, 4, 11, 7, 2, 3, 4$
Which one of the following statements is correct?
The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is
If l is the length of a diagonal of a cube of volume $V,$ then:
→In a $\triangle\text{ABC},$ if $\text{AB}=\text{AC}$ and BC is produced to D such that $\angle\text{ACD}=100^\circ$ then $\angle\text{A}=$
→Which of the following points does not lie in any quadrant?
The factors of $x^4 + x^2 + 25$ are:
→In $\triangle\text{ABC}$ and $\triangle\text{PQR},$ it is given that $AB = AC$, $\angle\text{C}=\angle\text{P}$ and $\angle\text{B}=\angle\text{Q}.$ Then, the two triangles are:
→Given $\angle\text{POR}=3\text{x}$ and $\angle\text{QOR}=2\text{x}+10^\circ.$If $POQ$ is a straight line, then the value of $x$ is:
→In the given figure, $ABC$ is an equilateral triangle. The value of $x + y$ is:
→