Question

Copy everything shown and supply missing statements and reasons.

Given:

$m\angle 1=m\angle 3$;

$m\angle 2=m\angle 4$

Prove: $m\angle ABC=m\angle DEF$

Proof:

Short answer

If $a=b$and $c=d$, then $a+c=b+d$.

$m\angle 1+m\angle 2=m\angle 3+m\angle 4$

Step-by-step solution

Step 1. Apply the addition property of algebra.

If $a=b$and $c=d$, then $a+c=b+d$.

$m\angle 1+m\angle 2=m\angle 3+m\angle 4$

Step 2. Angle addition postulate.

From the given figure, it can be observed that some of $m\angle 1$and $m\angle 2$gives $m\angle ABC$, that is $m\angle 1+m\angle 2=m\angle ABC$.

From the given figure, it can be observed that some of $m\angle 3$and $m\angle 4$gives $m\angle DEF$, that is $m\angle 3+m\angle 4=m\angle DEF$.

Step 3. Apply substitution property.

Substitute $m\angle ABC$for $m\angle 1+m\angle 2$and $m\angle DEF$for $m\angle 3+m\angle 4$in step 1.

$\begin{array}{c}m\angle 1+m\angle 2=m\angle 3+m\angle 4\\ m\angle ABC=m\angle DEF\end{array}$

Hence, it is proved that $m\angle ABC=m\angle DEF$.