Question

In the figure given above, $\angle B={38}^{\circ },AC=BC$ and $AD=CD$. What is $\angle D$ equal to?

• A. ${26}^{\circ }$
• B. ${28}^{\circ }$
• C. ${38}^{\circ }$
• D. ${52}^{\circ }$

Answer 1

The correct option is B ${28}^{\circ }$

Given, $AC=BC$
$\Rightarrow \angle A=\angle B$
$\Rightarrow \angle A={38}^{\circ }$
Therefore, $\angle ACB={180}^{\circ }-({38}^{\circ }+{38}^{\circ })={180}^{\circ }-{76}^{\circ }={104}^{\circ }$
$\Rightarrow \angle ACD=180-104={76}^{\circ }$
Also given $AD=CD$
$\Rightarrow \angle 2={76}^{\circ }$
In triangle $ACD,76+76+\angle D=180$
$\therefore \angle D={28}^{\circ }$