Question

given angles 1 and 2 are complementary
$m\angle1 = 36^{\circ}$
what is most likely being shown by the proof?
$\bigcirc$ a. $m\angle1 + m\angle3 = 90^{\circ}$
$\bigcirc$ b. $m\angle3 = 126^{\circ}$
$\bigcirc$ c. $m\angle3 = 144^{\circ}$
$\bigcirc$ d. $m\angle1 + m\angle3 = 180^{\circ}$

Explanation:

Step1: Solve for \(m\angle3\)

Given \(54^{\circ}+m\angle3 = 180^{\circ}\) (from substitution property of equality).
Subtract \(54^{\circ}\) from both sides: \(m\angle3=180^{\circ}- 54^{\circ}\).

Step2: Calculate the value

\(m\angle3 = 126^{\circ}\) (using subtraction operation).

Answer:

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