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Statement/Proof

∠2≅∠4, m∠2=110/Given
m∠2=m∠4/Definition of congruent angles
m∠4=110/what is this proof?
m∠3 and m∠4 are a linear pair/Definition of a linear pair (Shown in diagram)
m∠3 and m∠4 are supplementary/Linear Pair Postulate
m∠3+m∠4=180/what is this proof?
m∠3+110=180/Substitution Property
m∠3=70/what is this proof?

This proof proves that angle 3 has a measure of 70 degrees. The given information is that angle 2 has a measure of 110 degrees. Using the definition of congruent angles, we can conclude that angle 2 and angle 4 are congruent, which means they have the same measure. Then, we recognize that angles 3 and 4 are a linear pair, meaning they are adjacent angles that form a straight line. According to the Linear Pair Postulate, the measures of a linear pair of angles add up to 180 degrees. Therefore, we can write the equation m∠3 + m∠4 = 180. Substituting the measure of angle 4 as 110 degrees, we have m∠3 + 110 = 180. Finally, by subtracting 110 from both sides of the equation, we find that angle 3 has a measure of 70 degrees.