Question

pretest: foundations of geometry
given: ( mangle 1 = 110^circ )
( mangle 2 = 70^circ )
( angle 2 ) is supplementary to ( angle 3 )
prove: ( angle 1 cong angle 3 )
complete the proof.
congruent supplements theorem
given
definition of supplementary angles
linear pair theorem
transitive property of congruence
( mangle 1 = 110^circ )
( angle 1 ) is supplementary to ( angle 2 )
( angle 1 cong angle 3 )
( mangle 2 = 70^circ )
( angle 2 ) is supplementary to ( angle 3 )

Explanation:

Step1: Justify given angle measures

Reason: $\text{given}$

Step2: Prove $\angle1$ supplements $\angle2$

First, calculate $m\angle1 + m\angle2 = 110^\circ + 70^\circ = 180^\circ$.
Reason: $\text{definition of supplementary angles}$

Step3: Justify $\angle2$ supplements $\angle3$

Reason: $\text{given}$

Step4: Prove $\angle1 \cong \angle3$

Reason: $\text{congruent supplements theorem}$

Answer:

1. $m\angle1 = 110^\circ$: $\boldsymbol{\text{given}}$
2. $m\angle2 = 70^\circ$: $\boldsymbol{\text{given}}$
3. $\angle1$ is supplementary to $\angle2$: $\boldsymbol{\text{definition of supplementary angles}}$
4. $\angle2$ is supplementary to $\angle3$: $\boldsymbol{\text{given}}$
5. $\angle1 \cong \angle3$: $\boldsymbol{\text{congruent supplements theorem}}$