MCQ
Find the value of a given figure.
- A$12 \ cm.$
- B$6 \ cm.$
- ✓$10 \ cm.$
- D$15 \ cm.$
✓
Answer
Correct option: C.
$10 \ cm.$
Explanation :
Here, $\angle CAD =180^{\circ}-\left(130^{\circ}+25^{\circ}\right)=25^{\circ}$
Now, since $\angle CAD =\angle DAB$,
therefore, the $AD$ is the bisector of $\angle BAC$.
Since the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
$\therefore \frac{BD}{DC}=\frac{AB}{AC} $
$\Rightarrow \frac{x}{6}=\frac{15}{9}$
$\Rightarrow x=\frac{15 \times 6}{9}=10 \ cm$
Here, $\angle CAD =180^{\circ}-\left(130^{\circ}+25^{\circ}\right)=25^{\circ}$
Now, since $\angle CAD =\angle DAB$,
therefore, the $AD$ is the bisector of $\angle BAC$.
Since the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
$\therefore \frac{BD}{DC}=\frac{AB}{AC} $
$\Rightarrow \frac{x}{6}=\frac{15}{9}$
$\Rightarrow x=\frac{15 \times 6}{9}=10 \ cm$
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