Question

Copy everything shown and supply missing statements and reasons.

Given:$m\angle 4+m\angle 6=180$

Prove: $m\angle 5=m\angle 6$

Proof:

Short answer

When two lines intersect each other at a single point, they formed linear pair of angles. The sum of the linear pair of angles is always 180.

Step-by-step solution

Step 1. Apply the definition of linear pair of angles.

When two lines intersect each other at a single point, they formed linear pair of angles. The sum of the linear pair of angles is always 180.

Step 2. Description of step.

From the given figure, it can be observed that $\angle 4$and $\angle 5$form a linear pair of angles, that is, the sum of $\angle 4$and $\angle 5$is 180.

$m\angle 4+m\angle 5=180$

Step 3. Apply substitution property of algebra.

Substitute $m\angle 4+m\angle 5$for 180 into $m\angle 4+m\angle 6=180$.

$m\angle 4+m\angle 5=m\angle 4+m\angle 6$

Step 4. Reflexive property.

By reflexive property, $m\angle 4=m\angle 4$.

Step 4. Apply subtraction property of algebra to step 3.

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

$\begin{array}{c}m\angle 4+m\angle 5=m\angle 4+m\angle 6\\ m\angle 5=m\angle 6\end{array}$

Hence, it is proved that $m\angle 5=m\angle 6$.