Question

In Figure, we have $\angle ABC=\angle ACB$ and $\angle 3=\angle 4.$Show that $\angle 1=\angle 2.$

Answer 1

Step: Proving $\angle 1=\angle 2$

Given: $\angle ABC=\angle ACB\dots \left(i\right)$
and $\angle 4=\angle 3\dots \left(ii\right)$
Subtracting $\left(ii\right)$ from $\left(i\right),$ we get



$\angle ABC-\angle 4=\angle ACB-\angle 3$
$[\because$ If equals are subtracted from equals, then remainders are also equal $]$$\Rightarrow \angle 1=\angle 2$
Hence, proved.