Question

given: ∠1 and ∠2 are supplements, and ∠3 and ∠2 are supplements
prove: ∠1 ≅ ∠3
complete the missing parts of the paragraph proof.
by the definition of angles, the sum of the measures of angles 1 and 2 is 180 degrees. likewise, the sum of the measures of angles is 180 degrees. by the property, ( m∠1 + m∠2 = m∠3 + m∠2 ). subtract the measure of angle from each side. you get ( m∠1 = m∠3 ), or ( ∠1 ≅ ∠3 ), by the definition of congruence.

Explanation:

• The first blank: Since ∠1 and ∠2 are supplements, by the definition of supplementary angles (angles whose sum is \(180^{\circ}\)), the sum of their measures is \(180^{\circ}\).
• The second blank: Given ∠3 and ∠2 are supplements, so the sum of the measures of angles 3 and 2 is \(180^{\circ}\).
• The third blank: We have \(m\angle1 + m\angle2=m\angle3 + m\angle2\). This is an application of the substitution property (because both \(m\angle1 + m\angle2\) and \(m\angle3 + m\angle2\) equal \(180^{\circ}\), so we can substitute \(180^{\circ}\) with each other, or more precisely, since \(m\angle1 + m\angle2 = 180\) and \(m\angle3 + m\angle2=180\), we substitute \(180\) in the equation \(m\angle1 + m\angle2=m\angle3 + m\angle2\)).
• The fourth blank: To get \(m\angle1=m\angle3\) from \(m\angle1 + m\angle2=m\angle3 + m\angle2\), we subtract the measure of angle 2 from each side.

Answer:

1. supplementary
2. \(3\) and \(2\)
3. substitution
4. \(2\)