Question

∠1 and ∠2 are complementary
36° + m∠2 = 90°
m∠2 = 54°
given
definition of complementary angles
subtraction property of equality
m∠1 = 36°
54° + m∠3 = 180°
?
given
substitution property of equality
∠2 and ∠3 are a linear pair
m∠2 + m∠3 = 180°
given
linear pairs theorem
what is most likely being shown by the proof?
a. m∠3 = 126°
b. m∠1 + m∠3 = 180°
c. m∠1 + m∠3 = 90°
d. m∠3 = 144°

Explanation:

Step1: Solve for \(m\angle3\)

Given \(54^{\circ}+m\angle3 = 180^{\circ}\).
Using the subtraction property of equality (\(a + b=c\) implies \(b=c - a\)), we have \(m\angle3=180^{\circ}-54^{\circ}\).

Step2: Calculate the value

\(m\angle3 = 126^{\circ}\) (since \(180 - 54=126\)).

Answer:

A. \(m\angle3 = 126^{\circ}\)