Menu Close

Question-189715




Question Number 189715 by Rupesh123 last updated on 20/Mar/23
Answered by som(math1967) last updated on 21/Mar/23
△ABC≅△DBE  ⇒AB=DB  BC=BE ⇒∠BEC=∠BCE  ∠ACB=34 [∠ACB=∠CBE]    ∠DEB=∠ACB=34  AC∥BE  ∠ACE+∠BEC=180  34+x+x+34+34=180  2x=180−102  x=39
$$\bigtriangleup{ABC}\cong\bigtriangleup{DBE} \\ $$$$\Rightarrow{AB}={DB} \\ $$$${BC}={BE}\:\Rightarrow\angle{BEC}=\angle{BCE} \\ $$$$\angle{ACB}=\mathrm{34}\:\left[\angle{ACB}=\angle{CBE}\right]\:\: \\ $$$$\angle{DEB}=\angle{ACB}=\mathrm{34} \\ $$$${AC}\parallel{BE}\:\:\angle{ACE}+\angle{BEC}=\mathrm{180} \\ $$$$\mathrm{34}+{x}+{x}+\mathrm{34}+\mathrm{34}=\mathrm{180} \\ $$$$\mathrm{2}{x}=\mathrm{180}−\mathrm{102} \\ $$$${x}=\mathrm{39} \\ $$
Commented by Rupesh123 last updated on 21/Mar/23
Triangle ABC = Triangle DBE it implies that AB= DE, why?
Commented by som(math1967) last updated on 28/Mar/23
AB=DB [corresponding part  of congruence triangle]
$${AB}={DB}\:\left[{corresponding}\:{part}\right. \\ $$$$\left.{of}\:{congruence}\:{triangle}\right] \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *