Question

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

Explanation:

Step1: Solve for $m\angle3$

Use subtraction property of equality:
$m\angle3 = 180^\circ - 54^\circ$

Step2: Calculate the value

Compute the difference:
$m\angle3 = 126^\circ$

Answer:

A. $m\angle3 = 126^\circ$