Question

In $\Delta ABC,\overline{BC}$ is produced to E and $\angle ACE=13{\text{0}}^{\text{o}},$ If D is a point on $\overline{BC}$ such that $\overline{BD}=\overline{AD}=\overline{DC},$ then $\angle ABC=$

• A. $\text{8}{\text{0}}^{\text{o}}$
• B. $\text{4}{\text{0}}^{\text{o}}$
• C. $\text{6}{\text{0}}^{\text{o}}$
• D. $\text{7}{\text{0}}^{\text{o}}$

Answer 1

Answer: (B)

$\text{4}{\text{0}}^{\text{o}}$

REF.Image

$A+B+50=180$

$A+B={130}^{\circ }$

$\angle BAD+\angle ABD+100=180$

$\angle BAD=\angle ABD$

$\Rightarrow 2\angle ABC=80$

$\angle ABC={40}^{\circ }$