Question

In the given figure, what type of a triangle is $△ABC$, provided DB = AB and AC = CE?

• A. Equilateral
• B. Scalene
• C. Right-angled
• D. Isosceles

Answer 1

The correct option is B Scalene


Let $\angle DAB=\angle 1$ and $\angle CAE=\angle 2$.

$In△DAB,DB=AB\left(Given\right)\Rightarrow \angle BDA=\angle DAB$
$\Rightarrow \angle 1={35}^{\circ }$
(Angles opposite to equal sides are equal)
$Similarly,in△CAECE=AC\left(Given\right)\Rightarrow \angle CEA=\angle CAE$
$\Rightarrow \angle 2={46}^{\circ }$

$In\Delta CAE$,
$c=\angle CEA+\angle CAE$
(Since exterior angle of a triangle is equal to the sum of its two interior opposite angles)
$\Rightarrow c={46}^{\circ }+{46}^{\circ }$
$\Rightarrow c={92}^{\circ }$

$Similarly,in\Delta DAB$,
$b=\angle BDA+\angle BAD$
$\Rightarrow b={35}^{\circ }+{35}^{\circ }$
$\Rightarrow b={70}^{\circ }$

$In\Delta ABC$,
$a+b+c={180}^{\circ }$ (Sum of all the interior angles in a triangle is ${180}^{\circ }$)
$\Rightarrow a={180}^{\circ }-{70}^{\circ }-{92}^{\circ }$
$\Rightarrow a={18}^{\circ }$
Therefore $△ABC$ has 3 unequal angles and hence it is scalene.