$\angle1+\angle2+\angle3=180$

$\angle1+\angle3+\angle4=180$

$\angle4+\angle5+\angle6=180$

$\angle1+\angle4=\angle2$

Triangle Sum Theorem

Alternate Interior Angles Postulate

Vertical Angles Postulate

Exterior Angles Theorem

$\angle1+\angle2+\angle3=180$

$\angle1+\angle3+\angle4=180$

$\angle4+\angle5+\angle6=180$

$\angle1+\angle4=\angle2$

they are vertical.

they are complementary.

they are congruent.

they are supplementary.

$\angle4\cong\angle6$

$\angle1\cong\angle7$

$\angle2\cong\angle5$

$\angle4\cong\angle8$

$\angle4\cong\angle6$

$\angle1\cong\angle7$

$\angle2\cong\angle5$

$\angle4\cong\angle8$

 $m\angle K+m\angle L=90$  

 $m\angle K=m\angle L$  

 $m\angle K+m\angle L=180$  

 $m\angle K+180=m\angle L$  

the Alternate Angles Postulate

the Transitive property of Congruence

the Substitution property of Equality

the Vertical Angles Postulate

the Transitive Property of Equality

the Substitution Property of Equality

the Transitive Property of Congruence

the Linear Pair Postulate

$m\angle1+m\angle2+m\angle3=180$

$m\angle4+m\angle5+m\angle6=180$

$m\angle1+m\angle2+m\angle4=180$

$m\angle4+m\angle2+m\angle3=180$

$m\angle1=m\angle5$ by the Corresponding Angles Postulate

$m\angle2=m\angle5+m\angle6$ by the Corresponding Angles Postulate

$m\angle1=m\angle4+m\angle5$ by the Corresponding Angles Postulate

$m\angle3=m\angle6$ by the Corresponding Angles Postulate

$m\angle1=m\angle5$ by the Alternate Angles Postulate

$m\angle2=m\angle5+m\angle6$ by the Alternate Angles Postulate

$m\angle1=m\angle4+m\angle5$ by the Alternate Angles Postulate

$m\angle3=m\angle6$ by the Alternate Angles Postulate